reduce-historical/r36/xlog/SPECFN.LOG

REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...


%
%  Testing file for REDUCE Special Functions Package
%
%             Chris Cannam, ZIB Berlin
%             October 1992 -> Feb 1993
%        (only some of the time, of course)
%
%  Corrections and comments to neun@sc.zib-berlin.de
%


on savesfs;

     % just in case it's off for some reason

off bfspace;

    % to provide more similarity between runs
                % with old & new bigfloats

let {sinh (~x) => (exp(x) - exp (-x))/2 };


                % this will improve some results


% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     1. Bernoulli numbers

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


off rounded;



procedure do!*one!*bern(x);
   write ("Bernoulli ", x, " is ", bernoulli x);


do*one*bern


do!*one!*bern(1);


                 - 1
Bernoulli 1 is ------
                 2

do!*one!*bern(2);


                1
Bernoulli 2 is ---
                6

do!*one!*bern(3);


Bernoulli 3 is 0

do!*one!*bern(13);


Bernoulli 13 is 0

do!*one!*bern(14);


                 7
Bernoulli 14 is ---
                 6

do!*one!*bern(300);


Bernoulli 300 is ( - 
1863878995204859011995045341848156066182191846635905937518715320655775958174360523134990756922303410810482600528769479642021001218415879006164302955370460829146434807964717737195356935144151583424833154250047747433575584999029126775186293388721514970183351129809976971603227633930434923843984829580311593372565398574762880028289167635570012415606941367995702212211519561707046505473575241
                                                                    )/

                 866054419230

do!*one!*bern(-2);


Bernoulli -2 is bernoulli(-2)

do!*one!*bern(0);


Bernoulli 0 is 1


for n := 2 step 2 until 100 do do!*one!*bern n;


                1
Bernoulli 2 is ---
                6

                 - 1
Bernoulli 4 is ------
                 30

                1
Bernoulli 6 is ----
                42

                 - 1
Bernoulli 8 is ------
                 30

                 5
Bernoulli 10 is ----
                 66

                  - 691
Bernoulli 12 is --------
                  2730

                 7
Bernoulli 14 is ---
                 6

                  - 3617
Bernoulli 16 is ---------
                   510

                 43867
Bernoulli 18 is -------
                  798

                  - 174611
Bernoulli 20 is -----------
                    330

                 854513
Bernoulli 22 is --------
                  138

                  - 236364091
Bernoulli 24 is --------------
                     2730

                 8553103
Bernoulli 26 is ---------
                    6

                  - 23749461029
Bernoulli 28 is ----------------
                      870

                 8615841276005
Bernoulli 30 is ---------------
                     14322

                  - 7709321041217
Bernoulli 32 is ------------------
                       510

                 2577687858367
Bernoulli 34 is ---------------
                       6

                  - 26315271553053477373
Bernoulli 36 is -------------------------
                         1919190

                 2929993913841559
Bernoulli 38 is ------------------
                        6

                  - 261082718496449122051
Bernoulli 40 is --------------------------
                          13530

                 1520097643918070802691
Bernoulli 42 is ------------------------
                          1806

                  - 27833269579301024235023
Bernoulli 44 is ----------------------------
                            690

                 596451111593912163277961
Bernoulli 46 is --------------------------
                           282

                  - 5609403368997817686249127547
Bernoulli 48 is ---------------------------------
                              46410

                 495057205241079648212477525
Bernoulli 50 is -----------------------------
                             66

                  - 801165718135489957347924991853
Bernoulli 52 is -----------------------------------
                               1590

                 29149963634884862421418123812691
Bernoulli 54 is ----------------------------------
                               798

                  - 2479392929313226753685415739663229
Bernoulli 56 is ---------------------------------------
                                  870

                 84483613348880041862046775994036021
Bernoulli 58 is -------------------------------------
                                 354

                  - 1215233140483755572040304994079820246041491
Bernoulli 60 is ------------------------------------------------
                                    56786730

                 12300585434086858541953039857403386151
Bernoulli 62 is ----------------------------------------
                                   6

                  - 106783830147866529886385444979142647942017
Bernoulli 64 is -----------------------------------------------
                                      510

                 1472600022126335654051619428551932342241899101
Bernoulli 66 is ------------------------------------------------
                                     64722

                  - 78773130858718728141909149208474606244347001
Bernoulli 68 is -------------------------------------------------
                                       30

                 1505381347333367003803076567377857208511438160235
Bernoulli 70 is ---------------------------------------------------
                                       4686

                  - 5827954961669944110438277244641067365282488301844260429
Bernoulli 72 is ------------------------------------------------------------
                                         140100870

                 34152417289221168014330073731472635186688307783087
Bernoulli 74 is ----------------------------------------------------
                                         6

                  - 24655088825935372707687196040585199904365267828865801
Bernoulli 76 is ----------------------------------------------------------
                                            30

                 414846365575400828295179035549542073492199375372400483487
Bernoulli 78 is -----------------------------------------------------------
                                           3318

Bernoulli 80 is ( - 

                 4603784299479457646935574969019046849794257872751288919656867)/

                230010

                 1677014149185145836823154509786269900207736027570253414881613
Bernoulli 82 is ---------------------------------------------------------------
                                              498

Bernoulli 84 is ( - 

2024576195935290360231131160111731009989917391198090877281083932477
                                                                   )/3404310

Bernoulli 86 is 660714619417678653573847847426261496277830686653388931761996983/

                6

Bernoulli 88 is ( - 

1311426488674017507995511424019311843345750275572028644296919890574047
                                                                      )/61410

Bernoulli 90 is 

1179057279021082799884123351249215083775254949669647116231545215727922535
                                                                         /272118

Bernoulli 92 is ( - 

1295585948207537527989427828538576749659341483719435143023316326829946247
                                                                         )/1410

Bernoulli 94 is 

1220813806579744469607301679413201203958508415202696621436215105284649447
                                                                         /6

Bernoulli 96 is ( - 
211600449597266513097597728109824233673043954389060234150638733420050668349987259
 )/4501770

Bernoulli 98 is 

67908260672905495624051117546403605607342195728504487509073961249992947058239
                                                                             /6

Bernoulli 100 is ( - 
94598037819122125295227433069493721872702841533066936133385696204311395415197247711
   )/33330


on rounded;


precision 100;


12


do!*one!*bern(1);


Bernoulli 1 is  - 0.5

do!*one!*bern(2);


Bernoulli 2 is 0.166666666666666666666666666666666666666666666666666666666666666

               6666666666666666666666666666666666667

do!*one!*bern(3);


Bernoulli 3 is 0

do!*one!*bern(13);


Bernoulli 13 is 0

do!*one!*bern(14);


Bernoulli 14 is 1.16666666666666666666666666666666666666666666666666666666666666

                6666666666666666666666666666666666667

do!*one!*bern(300);


Bernoulli 300 is  - 2.1521499732799868297198173767560881985734565727838067018493

                 43925846796995824343474766557085976828531e+375

do!*one!*bern(-2);


Bernoulli -2 is bernoulli(-2)

do!*one!*bern(0);


Bernoulli 0 is 1

do!*one!*bern(38);


Bernoulli 38 is 4.88332318973593166666666666666666666666666666666666666666666666

                6666666666666666666666666666666666667e+14

do!*one!*bern(400);


Bernoulli 400 is  - 6.8469448558064533606162585823108835976782300971806257424147

                 81150311357197834589950328990573681886442e+549



% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     2. Gamma function

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


on rounded;


off complex;


precision 40;


100


algebraic procedure wg(x);
   write ("gamma (", x, ")  ==>  ", gamma x);


wg


algebraic procedure wp(x);
   write ("-- precision ", x, ",  from ", precision(x));


wp


wg (1/2);


gamma (0.5)  ==>  1.772453850905516027298167483341145182798

wg (3/2);


gamma (1.5)  ==>  0.8862269254527580136490837416705725913988


write ("sqrt(pi)/2  ==>  ", sqrt(pi)/2);


sqrt(pi)/2  ==>  0.8862269254527580136490837416705725913988


wp(10);


-- precision 10,  from 40


for x := 0 step 5 until 100 do
   << wg (1 + x/1000);
      wg (-1 - x/13);
      wp (8+floor(x/4)) >>;


gamma (1)  ==>  1

gamma (-1)  ==>  gamma(-1)

-- precision 8,  from 10

gamma (1.005)  ==>  0.99713854

gamma ( - 1.3846154)  ==>  2.7320314

-- precision 9,  from 8

gamma (1.01)  ==>  0.994325851

gamma ( - 1.76923077)  ==>  2.89933597

-- precision 10,  from 9

gamma (1.015)  ==>  0.9915612888

gamma ( - 2.153846154)  ==>   - 2.919307224

-- precision 11,  from 10

gamma (1.02)  ==>  0.98884420326

gamma ( - 2.5384615385)  ==>   - 0.91247160689

-- precision 13,  from 11

gamma (1.025)  ==>  0.9861739631483

gamma ( - 2.923076923077)  ==>   - 2.407817725014

-- precision 14,  from 13

gamma (1.03)  ==>  0.98354995055382

gamma ( - 3.3076923076923)  ==>  0.42665848359037

-- precision 15,  from 14

gamma (1.035)  ==>  0.980971560550586

gamma ( - 3.69230769230769)  ==>  0.250121998146955

-- precision 16,  from 15

gamma (1.04)  ==>  0.9784382009142447

gamma ( - 4.076923076923077)  ==>   - 0.4868211588210416

-- precision 18,  from 16

gamma (1.045)  ==>  0.975949291822951489

gamma ( - 4.46153846153846154)  ==>   - 0.064315864992688343

-- precision 19,  from 18

gamma (1.05)  ==>  0.9735042655627756432

gamma ( - 4.846153846153846154)  ==>   - 0.07308480130893001268

-- precision 20,  from 19

gamma (1.055)  ==>  0.9711025662416699039

gamma ( - 5.2307692307692307692)  ==>  0.026504298643014994546

-- precision 21,  from 20

gamma (1.06)  ==>  0.968743649511638364209

gamma ( - 5.61538461538461538462)  ==>  0.00947958151841097406813

-- precision 23,  from 21

gamma (1.065)  ==>  0.96642698229883993296188

gamma (-6)  ==>  gamma(-6)

-- precision 24,  from 23

gamma (1.07)  ==>  0.964152042541366448869499

gamma ( - 6.38461538461538461538462)  ==>   - 0.00224562428754660955672785

-- precision 25,  from 24

gamma (1.075)  ==>  0.9619183189344448686422338

gamma ( - 6.769230769230769230769231)  ==>   - 0.0014913552210721080976799

-- precision 26,  from 25

gamma (1.08)  ==>  0.95972531068282223532653464

gamma ( - 7.1538461538461538461538462)  ==>  0.0009821350464726696000373901

-- precision 28,  from 26

gamma (1.085)  ==>  0.9575725272601010524841387298

gamma ( - 7.538461538461538461538461538)  ==>  0.0002081367552774423831456972591

-- precision 29,  from 28

gamma (1.09)  ==>  0.95545948817480124076971838245

gamma ( - 7.9230769230769230769230769231)  ==>  0.000383724703597219454150804519

77

-- precision 30,  from 29

gamma (1.095)  ==>  0.95338572274293305256571929565

gamma ( - 8.30769230769230769230769230769)  ==>  

 - 0.0000487302698231202992921248405302

-- precision 31,  from 30

gamma (1.1)  ==>  0.9513507698668731836292487177265

gamma ( - 8.692307692307692307692307692308)  ==>  

 - 0.00002092711689267207910068115762837

-- precision 33,  from 31


wg(1/1000000003);


gamma (0.000000000999999997000000008999999973)  ==>  1.0000000024227843360875231

3084681e+9


off rounded;



gamma(17/2);


 2027025*sqrt(pi)
------------------
       256

gamma(-17/2);


      - 512*pi
-------------------
 34459425*sqrt(pi)

gamma(4);


6

gamma(0);


gamma(0)

gamma(-4);


gamma(-4)

gamma(-17/3);


          6*pi
------------------------
                   17
 17*sqrt(3)*gamma(----)
                   3


p := gamma(x**2) * gamma(x-y**gamma(y)) - (1/(gamma(4*(x-y))));


             2            gamma(y)
      gamma(x )*gamma( - y         + x)*gamma(4*x - 4*y) - 1
p := --------------------------------------------------------
                         gamma(4*x - 4*y)

y := 1/4;


      1
y := ---
      4

p;


        2             1  gamma(1/4)
 gamma(x )*gamma( - (---)           + x)*gamma(4*x - 1) - 1
                      4
------------------------------------------------------------
                       gamma(4*x - 1)

x := 3;


x := 3

p;


                         1  gamma(1/4)
 146313216000*gamma( - (---)           + 3) - 1
                         4
------------------------------------------------
                    3628800

y := -3/8;


       - 3
y := ------
       8

p;


(128*(2490343877896875*sqrt(pi)

                   - 3  (8*pi)/(3*gamma(3/8)*sin((3*pi)/8))
              3*(------)                                    - 1
                   8
      *gamma(---------------------------------------------------) - 64))/(
                    - 3  (8*pi)/(3*gamma(3/8)*sin((3*pi)/8))
                 (------)
                    8

   7905853580625*sqrt(pi))


on rounded, complex;


*** Domain mode rounded changed to complex-rounded 

precision 50;


33


p;


 - 0.00000000058461000084165968732153392127582134179078414159599

 + 3.7721251013859508830301986850709684723938237902095e-60*i


off rounded, complex;


*** Domain mode complex-rounded changed to complex 

clear y;



p;


                 gamma(y)
 40320*gamma( - y         + 3)*gamma( - 4*y + 12) - 1
------------------------------------------------------
                  gamma( - 4*y + 12)




% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     3. Beta function.  Not very interesting

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


algebraic procedure do!*one!*beta(x,y);
   write ("Beta (", x, ",", y, ") = ", beta(x,y));


do*one*beta


do!*one!*beta(0,1);


Beta (0,1) = beta(0,1)

do!*one!*beta(2,-3);


Beta (2,-3) = beta(2,-3)

do!*one!*beta(3,2);


              1
Beta (3,2) = ----
              12

do!*one!*beta(a+b,(c+d)**(b-a));


                                                            b
                                                     (c + d)
                                 gamma(a + b)*gamma(----------)
                    b                                       a
             (c + d)                                 (c + d)
Beta (a + b,----------) = ---------------------------------------------
                    a                    a            a            b
             (c + d)              (c + d) *a + (c + d) *b + (c + d)
                           gamma(------------------------------------)
                                                      a
                                               (c + d)

do!*one!*beta(-3,4);


Beta (-3,4) = beta(-3,4)

do!*one!*beta(-3,2);


Beta (-3,2) = beta(-3,2)

do!*one!*beta(-3,-7.5);


           - 15               - 15
Beta (-3,-------) = beta(-3,-------)
            2                  2

do!*one!*beta((pi * 10), exp(5));


                          5
             5     gamma(e )*gamma(10*pi)
Beta (10*pi,e ) = ------------------------
                            5
                     gamma(e  + 10*pi)


on rounded;


precision 30;


50


do!*one!*beta(0,1);


Beta (0,1) = beta(0,1)

do!*one!*beta(2,-3);


Beta (2,-3) = beta(2,-3)

do!*one!*beta(3,2);


Beta (3,2) = 0.0833333333333333333333333333333

do!*one!*beta(a+b,(c+d)**(b-a));


                                                            b
                                                     (c + d)
                                 gamma(a + b)*gamma(----------)
                    b                                       a
             (c + d)                                 (c + d)
Beta (a + b,----------) = ---------------------------------------------
                    a                    a            a            b
             (c + d)              (c + d) *a + (c + d) *b + (c + d)
                           gamma(------------------------------------)
                                                      a
                                               (c + d)

do!*one!*beta(-3,4);


Beta (-3,4) = beta(-3,4)

do!*one!*beta(-3,2);


Beta (-3,2) = beta(-3,2)

do!*one!*beta(-3,-7.5);


Beta (-3, - 7.5) = beta(-3, - 7.5)

do!*one!*beta((pi * 10), exp(5));


Beta (31.4159265358979323846264338328,148.413159102576603421115580041) = 3.26162

024071771351768890966259e-37




% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     4. Pochhammer notation

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


off rounded;



pochhammer(4,5);


6720

pochhammer(-4,5);


      - 24
---------------
 factorial(-1)

pochhammer(4,-5);


 factorial(-2)
---------------
       6

pochhammer(-4,-5);


  - 1
-------
 15120

pochhammer(17/2,12);


 157783444591397625
--------------------
        4096

pochhammer(-17/2,12);


  - 516891375
--------------
     4096

pochhammer(1/3,14)*pochhammer(2/3,15);


 148260333813553014031851192320000000
--------------------------------------
            68630377364883


q := pochhammer(1/5,11)*pochhammer(2/5,11)*pochhammer(3/5,11)*
      pochhammer(1-1/5,11)*pochhammer(1,11)*pochhammer(6/5,11)*
       pochhammer(70/50,11)*pochhammer(8/5,11)*pochhammer(9/5,11);


q := 
30835943859725167092317151562947659325673016884166249458427053145347526260421323040989302952930905614937458388095527696384131072
                                                /

     1292469707114105741986576081359316958696581423282623291015625


on complex;



pochhammer(a+b*i,c)*pochhammer(a-b*i,c);


pochhammer(a - i*b,c)*pochhammer(a + i*b,c)


a := 2;


a := 2

b := 3;


b := 3

c := 5;


c := 5


pochhammer(a+b*i,c)*pochhammer(a-b*i,c);


8950500


off complex;


on rounded;



pochhammer(1/5,11)*pochhammer(2/5,11)*pochhammer(3/5,11)*
 pochhammer(1-1/5,11)*pochhammer(1,11)*pochhammer(6/5,11)*
  pochhammer(70/50,11)*pochhammer(8/5,11)*pochhammer(9/5,11);


2.38581559706937212593793381562e+67


q;


2.38581559706937212593793381562e+67


pochhammer(pi,floor (pi**8));


2.47253079057195612235973919163e+33625

pochhammer(-pi,floor (pi**7));


5.91750008101140123889628058136e+9185

pochhammer(1.5,floor (pi**8));


1.88808885937650373473836451368e+33619




% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     5. Digamma function

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


procedure do!*one!*psi(x);
   << precision (precision(0) + 4)$
      write("Psi of ", x, " is ", psi(x) ) >> ;


do*one*psi


clear x, y;



z := x * ((x+y)**2 + (x**y));


         y    2            2
z := x*(x  + x  + 2*x*y + y )


off rounded;



do!*one!*psi(3);


                             1
             2*log(2) + psi(---) + psi(1) + 3
                             2
Psi of 3 is ----------------------------------
                            2

do!*one!*psi(pi);


Psi of pi is psi(pi)

do!*one!*psi(1.005);


        201           1
Psi of ----- is psi(-----) + 200
        200          200

do!*one!*psi(1.995);


                          pi                   1
                 199*cot(-----)*pi + 199*psi(-----) + 200
        399               200                 200
Psi of ----- is ------------------------------------------
        200                        199

do!*one!*psi(74);


Psi of 74 is (269426837164032294756360054754050*log(2)

                                                        1
               + 134713418582016147378180027377025*psi(---)
                                                        2

               + 2138308231460573767907619482175*psi(1)

               + 667084944417653637854891458725877)/

             136851726813476721146087646859200

do!*one!*psi(-1/2);


         - 1          1
Psi of ------ is psi(---) + 2
         2            2

do!*one!*psi(-3);


Psi of -3 is infinity

do!*one!*psi(z);


           y    2            2          y      3      2        2
Psi of x*(x  + x  + 2*x*y + y ) is psi(x *x + x  + 2*x *y + x*y )


on rounded;


precision 100;


62


do!*one!*psi(3);


Psi of 3 is 0.922784335098467139393487909917597568957840664060076401194232765115

            13227322233532906305293670825325048537

do!*one!*psi(pi);


Psi of 3.14159265358979323846264338327950288419716939937510582097494459230781640

       628620899862803482534211706798214809 is 0.9772133079420067332920694864061

82343640834609994325638009523286531810592477714131730207565436292873435576949

do!*one!*psi(1.005);


Psi of 1.005 is  - 0.56902091134438283168829569095002880926796887026346909469924

                37771372094405771031990077045450115105840960011306543

do!*one!*psi(1.995);


Psi of 1.995 is 0.41955460302810862865162027228724395469212997650340596127576800

                237211077024989654159358528162438486780461247996589393

do!*one!*psi(74);


Psi of 74 is 4.29729311880466763910635036256036713791964393500098361596464857079

             142072638532815275329153012799334519059885201047316254

do!*one!*psi(-1/2);


Psi of  - 0.5 is 0.0364899739785765205590236670012444328068403953395658929528727

                 461283450292829458978513262827154158754013655907090515460516684

                 6

do!*one!*psi(-3);


Psi of -3 is infinity

do!*one!*psi(z);


           y    2            2          y      3      2        2
Psi of x*(x  + x  + 2*x*y + y ) is psi(x *x + x  + 2*x *y + x*y )


precision 15;


132


x := 8/3;


x := 2.66666666666667

y := 7/1000;


y := 0.007

do!*one!*psi(z);


Psi of 21.74768766103287773 is 3.056340330052438423


off rounded;



clear x, y;



df(psi(z), x);


             y      3      2        2    y      y      2            2
polygamma(1,x *x + x  + 2*x *y + x*y )*(x *y + x  + 3*x  + 4*x*y + y )

df(df(psi(z), y),x);


 2*y                     y      3      2        2
x   *log(x)*polygamma(2,x *x + x  + 2*x *y + x*y )*x*y

    2*y                     y      3      2        2
 + x   *log(x)*polygamma(2,x *x + x  + 2*x *y + x*y )*x

      y                     y      3      2        2   3
 + 3*x *log(x)*polygamma(2,x *x + x  + 2*x *y + x*y )*x

      y                     y      3      2        2   2
 + 4*x *log(x)*polygamma(2,x *x + x  + 2*x *y + x*y )*x *y

    y                     y      3      2        2     2
 + x *log(x)*polygamma(2,x *x + x  + 2*x *y + x*y )*x*y

    y                     y      3      2        2
 + x *log(x)*polygamma(1,x *x + x  + 2*x *y + x*y )*y

    y                     y      3      2        2
 + x *log(x)*polygamma(1,x *x + x  + 2*x *y + x*y )

      y              y      3      2        2   2
 + 2*x *polygamma(2,x *x + x  + 2*x *y + x*y )*x *y

      y              y      3      2        2   2
 + 2*x *polygamma(2,x *x + x  + 2*x *y + x*y )*x

      y              y      3      2        2     2
 + 2*x *polygamma(2,x *x + x  + 2*x *y + x*y )*x*y

      y              y      3      2        2
 + 2*x *polygamma(2,x *x + x  + 2*x *y + x*y )*x*y

    y              y      3      2        2
 + x *polygamma(1,x *x + x  + 2*x *y + x*y )

                  y      3      2        2   4
 + 6*polygamma(2,x *x + x  + 2*x *y + x*y )*x

                   y      3      2        2   3
 + 14*polygamma(2,x *x + x  + 2*x *y + x*y )*x *y

                   y      3      2        2   2  2
 + 10*polygamma(2,x *x + x  + 2*x *y + x*y )*x *y

                  y      3      2        2     3
 + 2*polygamma(2,x *x + x  + 2*x *y + x*y )*x*y

                  y      3      2        2
 + 4*polygamma(1,x *x + x  + 2*x *y + x*y )*x

                  y      3      2        2
 + 2*polygamma(1,x *x + x  + 2*x *y + x*y )*y

int(psi(z), z);


           y      3      2        2
log(gamma(x *x + x  + 2*x *y + x*y ))


on rounded;



for k := 1 step 0.1 until 2 do do!*one!*psi(k);


Psi of 1 is  - 0.57721566490153286060651

Psi of 1.09999999999999999999999999 is  - 0.423754940411076795168216226

Psi of 1.19999999999999999999999999483 is  - 0.2890398965921882955472079690017

Psi of 1.2999999999999999999999999948304368 is 

 - 0.16919088886679965563116117990224309

Psi of 1.39999999999999999999999999483043679294 is 

 - 0.0613845445851161457306754873481741603465

Psi of 1.499999999999999999999999994830436792938162 is 0.03648997397857652055902

366216872537099062413

Psi of 1.5999999999999999999999999948304367929381615219 is 0.1260474527734762519

0600271342271679469086378102

Psi of 1.69999999999999999999999999483043679293816152191799 is 0.208547874873493

95667996417990930337500109911872963

Psi of 1.799999999999999999999999994830436792938161521917991479 is 0.28499143329

38615406087023630333301945809176983421812009

Psi of 1.8999999999999999999999999948304367929381615219179914789724 is 0.3561841

6116405971922472708037210055174041765918986424485621

Psi of 1.99999999999999999999999999483043679293816152191799147897240477 is 0.422

784335098467139393487906583570145998489083710421411058968004


off rounded;



% PSI_SIMP.TST  F.J.Wright, 2 July 1993

on evallhseqp;


factor psi;

  on rat, intstr, div;

  % for neater output
% Do not try using "off mcd"!

psi(x+m) - psi(x+m-1) = 1/(x+m-1);


     1           1
-----------=-----------
 m + x - 1   m + x - 1

psi(x+2) - psi(x+1) + 2*psi(x) = 1/(x+1) + 2*psi(x);


              1                  1
2*psi(x) + -------=2*psi(x) + -------
            x + 1              x + 1

psi(x+2) + 3*psi(x) = 4*psi(x) + 1/x + 1/(x+1);


             -1                   -1
            x   + 2              x   + 2
4*psi(x) + ---------=4*psi(x) + ---------
             x + 1                x + 1


psi(x + 1) = psi(x) + 1/x;


          -1           -1
psi(x) + x  =psi(x) + x

psi(x + 3/2) = psi(x + 1/2) + 1/(x + 1/2);


         1         2              1         2
psi(x + ---) + ---------=psi(x + ---) + ---------
         2      2*x + 1           2      2*x + 1

psi(x - 1/2) = psi(x + 1/2) - 1/(x - 1/2);


         1         2              1         2
psi(x + ---) - ---------=psi(x + ---) - ---------
         2      2*x - 1           2      2*x - 1

psi((x + 3a)/a);


                          -1
     1        2*(3*x + 8*x   + 12)
psi(---*x) + ----------------------
     2             2
                  x  + 6*x + 8
  psi(x/y + 3);


                          -1  2
       -1     y*(3*x + 2*x  *y  + 6*y)
psi(x*y  ) + --------------------------
                  2              2
                 x  + 3*x*y + 2*y


off rat, intstr, div;

  on rational;



psi(x+m) - psi(x+m-1) = 1/(x+m-1);


     1           1
-----------=-----------
 m + x - 1   m + x - 1

psi(x+2) - psi(x+1) + 2*psi(x) = 1/(x+1) + 2*psi(x);


 2*psi(x)*x + 2*psi(x) + 1   2*psi(x)*x + 2*psi(x) + 1
---------------------------=---------------------------
           x + 1                       x + 1

psi(x+2) + 3*psi(x) = 4*psi(x) + 1/x + 1/(x+1);


           2                                    2
 4*psi(x)*x  + 4*psi(x)*x + 2*x + 1   4*psi(x)*x  + 4*psi(x)*x + 2*x + 1
------------------------------------=------------------------------------
                2                                    2
               x  + x                               x  + x


psi(x + 1) = psi(x) + 1/x;


 psi(x)*x + 1   psi(x)*x + 1
--------------=--------------
      x              x

psi(x + 3/2) = psi(x + 1/2) + 1/(x + 1/2);


          1        1           1                  1        1           1
 psi(x + ---)*x + ---*psi(x + ---) + 1   psi(x + ---)*x + ---*psi(x + ---) + 1
          2        2           2                  2        2           2
---------------------------------------=---------------------------------------
                     1                                       1
                x + ---                                 x + ---
                     2                                       2

psi(x - 1/2) = psi(x + 1/2) - 1/(x - 1/2);


          1        1           1                  1        1           1
 psi(x + ---)*x - ---*psi(x + ---) - 1   psi(x + ---)*x - ---*psi(x + ---) - 1
          2        2           2                  2        2           2
---------------------------------------=---------------------------------------
                     1                                       1
                x - ---                                 x - ---
                     2                                       2

psi((x + 3a)/a);


      1         2                  2          8
 psi(---*x)*x*(x  + 6*x + 8) + 6*(x  + 4*x + ---)
      2                                       3
--------------------------------------------------
                     2
                 x*(x  + 6*x + 8)
  psi(x/y + 3);


      x       2              2          2            2   2
 psi(---)*x*(x  + 3*x*y + 2*y ) + 3*y*(x  + 2*x*y + ---*y )
      y                                              3
------------------------------------------------------------
                       2              2
                   x*(x  + 3*x*y + 2*y )


off rational;



% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     6. Polygamma functions

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


procedure do!*one!*pg(n,x);
   write ("Polygamma (", n, ") of ", x, " is ", polygamma(n,x));


do*one*pg


off rounded;



do!*one!*pg(1,1/2);


                  1                  1
Polygamma (1) of --- is polygamma(1,---)
                  2                  2

do!*one!*pg(1,1);


                         2
                       pi
Polygamma (1) of 1 is -----
                        6

do!*one!*pg(1,3/2);


                           2
                  3      pi  - 8
Polygamma (1) of --- is ---------
                  2         2

do!*one!*pg(1,1.005);


                  201                  201
Polygamma (1) of ----- is polygamma(1,-----)
                  200                  200

do!*one!*pg(1,1.995);


                  399                  399
Polygamma (1) of ----- is polygamma(1,-----)
                  200                  200

do!*one!*pg(1,1e-10);


                       1                            1
Polygamma (1) of ------------- is polygamma(1,-------------)
                  10000000000                  10000000000

do!*one!*pg(2,1.45);


                  29                  29
Polygamma (2) of ---- is polygamma(2,----)
                  20                  20

do!*one!*pg(3,1.99);


                  199                  199
Polygamma (3) of ----- is polygamma(3,-----)
                  100                  100

do!*one!*pg(4,-8.2);


                   - 41                   - 41
Polygamma (4) of ------- is polygamma(4,-------)
                    5                      5

do!*one!*pg(5,0);


Polygamma (5) of 0 is infinity

do!*one!*pg(6,-5);


Polygamma (6) of -5 is infinity

do!*one!*pg(7,200);


Polygamma (7) of 200 is (
17726903568079021516229662669344581999513453462651624712682433450930396569413638060869523209196416456149981841411350319061723276968944831274405326841106087088051862580482604049179034792880997036306450715491134920388121743532178874504889199026667348488846246287054278592284199023548572837863642592371308428279823642858774260678182876022899303888558378920013392172441409952343098219076353830605697314645020537255667718925997023946826863459069360054494011515187931095594830347819766125471751832158677864778297413490571816668099535649328289203181141151677544880676008798702466775519536091686976761627732998715124407667063278175501392084867643186474774933465396962161891279302009565617687762042880000000000000000000000
                                                                            8
                                                                         *pi  - 
168202274324609919911886603179553832485831631970776943913214724306758011473978941132413094748296521617074167117661053498983406945306976674698602419479427329202365001144489134708765120356232374484239386020849061429951991522474455058548094378661234695692419462486402225369012574020278308089090741397551205530205566242796380021997272735088025054393694714504643986352458446128585149055841912367918690170304028682697422603414064799513570602284100682485151815951427876744662169487167539572896985974962832514966524381217035170993953423670212502913136819535576467936946089479260579835796147751358821073694464012485544356514018523618843496912692835966265011413341612149624871304965950289830955139972163546512706990894178649281
                                                                             )/
33237944190148165342930617505021091249087725242471796336279562720494493567650571364130356017243280855281215952646281848240731144316771558639509987827073913290097242338404882592210690236651869443074595091545877975727728269122835389696667248175001278416586711788226772360532873169153574070994329860696203303024669330360201738771592892542936194791046960475025110323327643660643309160768163432385682464959413507354376972986244419900300368985755050102176271590977370804240306902162061485259534685297520996459307650294822156252686629342490542255964639659395396651267516497567125204099130171913081428051999372590858264375743646579065110159126830974640203000247619304053546148691267935533164553830400000000000000000000000


on rounded;


precision 100;


63


do!*one!*pg(1,1/2);


Polygamma (1) of 0.5 is 4.934802200544679309417245499938075567656849703620395313

206674688110022411209602621500886701859276116

do!*one!*pg(1,1);


Polygamma (1) of 1 is 1.64493406684822643647241516664602518921894990120679843773

5558229370007470403200873833628900619758705

do!*one!*pg(1,3/2);


Polygamma (1) of 1.5 is 0.934802200544679309417245499938075567656849703620395313

2066746881100224112096026215008867018592761159

do!*one!*pg(1,1.005);


Polygamma (1) of 1.005 is 1.6329941567556809752535869786110269899606654266292810

17423768306472667920740136690588658095268582677

do!*one!*pg(1,1.995);


Polygamma (1) of 1.995 is 0.6469608286405823512476399271078276952436864784225077

824256922477813603546774633500406650324443323374

do!*one!*pg(1,1e-10);


Polygamma (1) of 0.0000000001 is 1.000000000000000000016449340666078150558729660

065732639916420752057756424780180942170336642993019363e+20

do!*one!*pg(2,1.45);


Polygamma (2) of 1.45 is  - 0.90383740307625768823230953852986719286009030811144

6658245367522559171482627166928803699348863802546

do!*one!*pg(3,1.99);


Polygamma (3) of 1.99 is 0.50290713241686532018051099086257019718615168956130804

44480934082942919777908933506993776280887706183

do!*one!*pg(4,-8.2);


Polygamma (4) of  - 8.2 is 74935.51259577427052712029230781313552295905493466277

917617629718610711391593937121099755096024434196

do!*one!*pg(5,0);


Polygamma (5) of 0 is infinity

do!*one!*pg(6,-5);


Polygamma (6) of -5 is infinity

do!*one!*pg(7,200);


Polygamma (7) of 200 is 5.724093725392558373837029681544727245346807368195956154

743567847385926644129753317064645661270233713e-14


off rounded;


clear x;




% Polygamma differentiation has already
% been tried a bit in the psi section

df(int(int(int(polygamma(3,x),x),x),x),x);


polygamma(1,x)


clear w, y, z;





% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     7. Zeta function

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


procedure do!*one!*zeta(n);
   write ("Zeta of ", n, " is ", zeta n);


do*one*zeta


off rounded;


clear x, y, z;



z := x * ((x+y)**5 + (x**y));


         y    5      4         3  2       2  3        4    5
z := x*(x  + x  + 5*x *y + 10*x *y  + 10*x *y  + 5*x*y  + y )


do!*one!*zeta(0);


               - 1
Zeta of 0 is ------
               2


for k := 4 step 2 until 35 do 
   do!*one!*zeta(k);


                4
              pi
Zeta of 4 is -----
              90

                6
              pi
Zeta of 6 is -----
              945

                8
              pi
Zeta of 8 is ------
              9450

                 10
               pi
Zeta of 10 is -------
               93555

                     12
               691*pi
Zeta of 12 is -----------
               638512875

                    14
                2*pi
Zeta of 14 is ----------
               18243225

                       16
                3617*pi
Zeta of 16 is --------------
               325641566250

                         18
                 43867*pi
Zeta of 18 is ----------------
               38979295480125

                          20
                 174611*pi
Zeta of 20 is ------------------
               1531329465290625

                           22
                  155366*pi
Zeta of 22 is -------------------
               13447856940643125

                              24
                  236364091*pi
Zeta of 24 is -----------------------
               201919571963756521875

                             26
                   1315862*pi
Zeta of 26 is ----------------------
               11094481976030578125

                                28
                   6785560294*pi
Zeta of 28 is --------------------------
               564653660170076273671875

                                    30
                    6892673020804*pi
Zeta of 30 is ------------------------------
               5660878804669082674070015625

Zeta of 32 is zeta(32)

Zeta of 34 is zeta(34)


do!*one!*zeta(-17/3);


          - 17            - 17
Zeta of ------- is zeta(-------)
           3               3

do!*one!*zeta(190);


Zeta of 190 is zeta(190)

do!*one!*zeta(300);


Zeta of 300 is zeta(300)

do!*one!*zeta(0);


               - 1
Zeta of 0 is ------
               2

do!*one!*zeta(-44);


Zeta of -44 is 0


on rounded;


clear x, y;



for k := 3 step 3 until 36 do <<
   precision (31+k*3);
   do!*one!*zeta(k) >>;


Zeta of 3 is 1.202056903159594285399738161511449990765

Zeta of 6 is 1.017343061984449139714517929790920527901817490033

Zeta of 9 is 1.002008392826082214417852769232412060485605851394888756549

Zeta of 12 is 1.0002460865533080482986379980477396709604160884580034045330409521

              33

Zeta of 15 is 1.0000305882363070204935517285106450625876279487068581775065699328

              93332267156

Zeta of 18 is 1.0000038172932649998398564616446219397304546972189533311431744299

              87630039542650045638

Zeta of 21 is 1.0000004769329867878064631167196043730459664466947849376002074873

              76596839087898159833876638564

Zeta of 24 is 1.0000000596081890512594796124402079358012275039188373027958642469

              72321724495355468544848206832825003614

Zeta of 27 is 1.0000000074507117898354294919810041706041194547190318825658299932

              39578352147606271570867900837100313523764933952

Zeta of 30 is 1.0000000009313274324196681828717647350212198135679551368161850086

              13360441960672940496363503624604027929086312123388047291

Zeta of 33 is 1.0000000001164155017270051977592973835456309516522471727635932565

              17739947029124624567548673934974376008810870912845774213829513369

Zeta of 36 is 1.0000000000145519218910419842359296322453184209838088941240380691

              395422185717458650302201529989423295781853630847913399997790928914

              91916899


precision 20;


139


do!*one!*zeta(-17/3);


Zeta of  - 5.6666666666666666667 is  - 0.0018766468228592287697

do!*one!*zeta(z);


            y    5      4         3  2       2  3        4    5
Zeta of x*(x  + x  + 5*x *y + 10*x *y  + 10*x *y  + 5*x*y  + y ) is zeta(

    y      6      5         4  2       3  3      2  4      5
   x *x + x  + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + x*y )


y := 3;


y := 3

x := pi;


x := 3.1415926535897932385


do!*one!*zeta(z);


Zeta of 27548.203250393209469 is 1

do!*one!*zeta(190);


Zeta of 190 is 1.0

do!*one!*zeta(300);


Zeta of 300 is 1

do!*one!*zeta(0);


Zeta of 0 is  - 0.5

do!*one!*zeta(-44);


Zeta of -44 is 0


off rounded;





% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     8. Kummer functions

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


off rounded;



t!*kummer!*a := { 1, 2.4, -1397/10  }$


t!*kummer!*b := { 0, 1, pi, -pi, 26 }$



for each a in t!*kummer!*a do
   for each b in t!*kummer!*a do
      for each z in t!*kummer!*a do
         << write "KummerM(", a, ",", b, ",", z, ") = ",
               kummerm(a,b,z);
            write "KummerU(", a, ",", b, ",", z, ") = ",
               kummeru(a,b,z) >>;


KummerM(1,1,1) = e

KummerU(1,1,1) = kummeru(1,1,1)

             12      2/5  2
KummerM(1,1,----) = e   *e
             5

             12                  12
KummerU(1,1,----) = kummeru(1,1,----)
             5                   5

              - 1397          1
KummerM(1,1,---------) = ------------
               10          7/10  139
                          e    *e

              - 1397                   - 1397
KummerU(1,1,---------) = kummeru(1,1,---------)
               10                       10

           12                  12
KummerM(1,----,1) = kummerm(1,----,1)
           5                   5

                              2           12                  12
                     2*gamma(---)*(gamma(----)*e - kummerm(1,----,1))
           12                 5           5                   5
KummerU(1,----,1) = --------------------------------------------------
           5                                   12
                                      5*gamma(----)
                                               5

           12   12                12   12
KummerM(1,----,----) = kummerm(1,----,----)
           5    5                 5    5

           12   12
KummerU(1,----,----) = 
           5    5

        2       2/5  2/5        12    2       4/5  2/5            12   12
 gamma(---)*(5*e   *5   *gamma(----)*e  - 12*2   *3   *kummerm(1,----,----))
        5                       5                                 5    5
-----------------------------------------------------------------------------
                              4/5  2/5        12
                          30*2   *3   *gamma(----)
                                              5

           12    - 1397                12    - 1397
KummerM(1,----,---------) = kummerm(1,----,---------)
           5      10                   5      10

           12    - 1397               2
KummerU(1,----,---------) = (2*gamma(---)*(
           5      10                  5

               7/10     2/5            12    - 1397    139
       - 1397*e    *1397   *kummerm(1,----,---------)*e
                                       5      10

              2/5        12            7/10     2/5        12    139
       - 10*10   *gamma(----)))/(6985*e    *1397   *gamma(----)*e   )
                         5                                 5

            - 1397                   - 1397
KummerM(1,---------,1) = kummerm(1,---------,1)
             10                       10

            - 1397
KummerU(1,---------,1) = 
             10

             1397               - 1397          3*pi
 1397*gamma(------)*kummerm(1,---------,1)*sin(------) - 10*e*pi
              10                 10              10
-----------------------------------------------------------------
                            1417        3*pi
                  10*gamma(------)*sin(------)
                             10          10

            - 1397   12                 - 1397   12
KummerM(1,---------,----) = kummerm(1,---------,----)
             10      5                   10      5

            - 1397   12
KummerU(1,---------,----) = ( - 
             10      5
48689401707698071401637346296148709517635305466315546784369062686038955387470672028214421172492426257970894859785608060010798787187515790195560655355904
                                                                          2/5
                                                                        *e

     2/5  7/10  2
   *2   *3    *e *pi + 
20045966895736519148343810333245571434480905551887283539400953780162950579324387945234775543212890625
                       7/10        1397               - 1397   12        3*pi
                     *5    *gamma(------)*kummerm(1,---------,----)*sin(------))
                                    10                 10      5          10

/(
143492962746861268062589909328887411843098822848155215027923792270314606867032125592231750488281250
                     7/10        1417        3*pi
                   *5    *gamma(------)*sin(------))
                                  10          10

            - 1397    - 1397                 - 1397    - 1397
KummerM(1,---------,---------) = kummerm(1,---------,---------)
             10        10                     10        10

            - 1397    - 1397
KummerU(1,---------,---------) = (1397*( - 
             10        10
152159982579315173600331019038628152238885433889572221061155552992026662790488679161680024820756008730757778143037042693923932846444113056473446432154278794079710763645820340853851602689287025084815217783532480956517472235723731181252401977856952544597761994384769996636245679210281354768553595796003820698711669598622602752713703151447293557592795912091076094345980353443096817710446904761297306235868715700448137787799653833690839289133
                                                7/10
                                      *( - 1397)    *pi + 
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
                                                              7/10   7/10
                                                            *e    *10

              1397               - 1397    - 1397        3*pi    139
      *gamma(------)*kummerm(1,---------,---------)*sin(------)*e   ))/(
               10                 10        10            10
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
                                                               7/10   7/10
                                                             *e    *10

           1417        3*pi    139
   *gamma(------)*sin(------)*e   )
            10          10

         12                  12
KummerM(----,1,1) = kummerm(----,1,1)
         5                   5

         12                  12
KummerU(----,1,1) = kummeru(----,1,1)
         5                   5

         12     12              12     12
KummerM(----,1,----) = kummerm(----,1,----)
         5      5               5      5

         12     12              12     12
KummerU(----,1,----) = kummeru(----,1,----)
         5      5               5      5

         12      - 1397              12      - 1397
KummerM(----,1,---------) = kummerm(----,1,---------)
         5        10                 5        10

         12      - 1397              12      - 1397
KummerU(----,1,---------) = kummeru(----,1,---------)
         5        10                 5        10

         12   12
KummerM(----,----,1) = e
         5    5

                                 2               - 2          2*pi
                        2*gamma(---)*kummerm(1,------,1)*sin(------) + 5*e*pi
         12   12                 5               5             5
KummerU(----,----,1) = -------------------------------------------------------
         5    5                                12        2*pi
                                      5*gamma(----)*sin(------)
                                               5          5

         12   12   12      2/5  2
KummerM(----,----,----) = e   *e
         5    5    5

         12   12   12
KummerU(----,----,----) = 
         5    5    5

    2/5  4/5  2/5  2       2/5        2               - 2   12        2*pi
 6*e   *2   *3   *e *pi + 5   *gamma(---)*kummerm(1,------,----)*sin(------)
                                      5               5     5          5
-----------------------------------------------------------------------------
                        4/5  2/5        12        2*pi
                     6*2   *3   *gamma(----)*sin(------)
                                        5          5

         12   12    - 1397          1
KummerM(----,----,---------) = ------------
         5    5      10          7/10  139
                                e    *e

         12   12    - 1397
KummerU(----,----,---------) = (
         5    5      10

         7/10   2/5        2               - 2    - 1397        2*pi    139
    - 4*e    *10   *gamma(---)*kummerm(1,------,---------)*sin(------)*e
                           5               5       10            5

               2/5            7/10     2/5        12        2*pi    139
    + 1397*1397   *pi)/(1397*e    *1397   *gamma(----)*sin(------)*e   )
                                                  5          5

         12    - 1397                12    - 1397
KummerM(----,---------,1) = kummerm(----,---------,1)
         5      10                   5      10

         12    - 1397                     1431            1431   1417
KummerU(----,---------,1) = ( - 10*gamma(------)*kummerm(------,------,1)*pi + 
         5      10                         10              10     10

               1417          1397          12            12    - 1397
   1397*gamma(------)*gamma(------)*gamma(----)*kummerm(----,---------,1)
                10            10           5             5      10

         3*pi               1431          1417          12        3*pi
   *sin(------))/(10*gamma(------)*gamma(------)*gamma(----)*sin(------))
          10                 10            10           5          10

         12    - 1397   12              12    - 1397   12
KummerM(----,---------,----) = kummerm(----,---------,----)
         5      10      5               5      10      5

         12    - 1397   12
KummerU(----,---------,----) = (
         5      10      5
20045966895736519148343810333245571434480905551887283539400953780162950579324387945234775543212890625
                       7/10        1417          1397          12
                     *5    *gamma(------)*gamma(------)*gamma(----)
                                    10            10           5

             12    - 1397   12        3*pi
   *kummerm(----,---------,----)*sin(------) - 
             5      10      5          10
48689401707698071401637346296148709517635305466315546784369062686038955387470672028214421172492426257970894859785608060010798787187515790195560655355904
                                                                          2/5
                                                                        *2

     7/10        1431            1431   1417   12
   *3    *gamma(------)*kummerm(------,------,----)*pi)/(
                  10              10     10    5
143492962746861268062589909328887411843098822848155215027923792270314606867032125592231750488281250
                     7/10        1431          1417          12        3*pi
                   *5    *gamma(------)*gamma(------)*gamma(----)*sin(------))
                                  10            10           5          10

         12    - 1397    - 1397              12    - 1397    - 1397
KummerM(----,---------,---------) = kummerm(----,---------,---------)
         5      10        10                 5      10        10

         12    - 1397    - 1397
KummerU(----,---------,---------) = (1397*( - 
         5      10        10
152159982579315173600331019038628152238885433889572221061155552992026662790488679161680024820756008730757778143037042693923932846444113056473446432154278794079710763645820340853851602689287025084815217783532480956517472235723731181252401977856952544597761994384769996636245679210281354768553595796003820698711669598622602752713703151447293557592795912091076094345980353443096817710446904761297306235868715700448137787799653833690839289133
                                                7/10        1431
                                      *( - 1397)    *gamma(------)
                                                             10

                1431   1417    - 1397
      *kummerm(------,------,---------)*pi + 
                 10     10      10
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
                                                               7/10
                                                            *10

              1417          1397          12            12    - 1397    - 1397
      *gamma(------)*gamma(------)*gamma(----)*kummerm(----,---------,---------)
               10            10           5             5      10        10

            3*pi
      *sin(------)))/(
             10
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
                                                                7/10
                                                             *10

           1431          1417          12        3*pi
   *gamma(------)*gamma(------)*gamma(----)*sin(------))
            10            10           5          10

          - 1397                   - 1397
KummerM(---------,1,1) = kummerm(---------,1,1)
           10                       10

          - 1397                   - 1397
KummerU(---------,1,1) = kummeru(---------,1,1)
           10                       10

          - 1397     12               - 1397     12
KummerM(---------,1,----) = kummerm(---------,1,----)
           10        5                 10        5

          - 1397     12               - 1397     12
KummerU(---------,1,----) = kummeru(---------,1,----)
           10        5                 10        5

          - 1397      - 1397               - 1397      - 1397
KummerM(---------,1,---------) = kummerm(---------,1,---------)
           10          10                   10          10

          - 1397      - 1397               - 1397      - 1397
KummerU(---------,1,---------) = kummeru(---------,1,---------)
           10          10                   10          10

          - 1397   12                 - 1397   12
KummerM(---------,----,1) = kummerm(---------,----,1)
           10      5                   10      5

          - 1397   12
KummerU(---------,----,1) = (
           10      5

               1411             - 1397   12          pi
   7055*gamma(------)*kummerm(---------,----,1)*sin(----)*pi + 2794
                10               10      5           10

           1397          12          2             - 1411    - 2          3*pi
   *gamma(------)*gamma(----)*gamma(---)*kummerm(---------,------,1)*sin(------)
            10           5           5              10       5             10

         2*pi               12        2*pi
   *sin(------))/(50*gamma(----)*sin(------)*pi)
          5                 5          5

          - 1397   12   12               - 1397   12   12
KummerM(---------,----,----) = kummerm(---------,----,----)
           10      5    5                 10      5    5

          - 1397   12   12            2/5        1397          12          2
KummerU(---------,----,----) = (1397*5   *gamma(------)*gamma(----)*gamma(---)
           10      5    5                         10           5           5

              - 1411    - 2   12        3*pi        2*pi
   *kummerm(---------,------,----)*sin(------)*sin(------)
               10       5     5          10          5

            4/5  2/5        1411             - 1397   12   12        pi
    + 8466*2   *3   *gamma(------)*kummerm(---------,----,----)*sin(----)*pi)/(
                             10               10      5    5         10

       4/5  2/5        12        2*pi
   60*2   *3   *gamma(----)*sin(------)*pi)
                       5          5

          - 1397   12    - 1397               - 1397   12    - 1397
KummerM(---------,----,---------) = kummerm(---------,----,---------)
           10      5      10                   10      5      10

          - 1397   12    - 1397
KummerU(---------,----,---------) = (
           10      5      10

            2/5        1411             - 1397   12    - 1397        pi
   1411*1397   *gamma(------)*kummerm(---------,----,---------)*sin(----)*pi - 4
                        10               10      5      10           10

      2/5        1397          12          2
   *10   *gamma(------)*gamma(----)*gamma(---)
                  10           5           5

              - 1411    - 2    - 1397        3*pi        2*pi            2/5
   *kummerm(---------,------,---------)*sin(------)*sin(------))/(10*1397
               10       5       10            10          5

           12        2*pi
   *gamma(----)*sin(------)*pi)
           5          5

          - 1397    - 1397
KummerM(---------,---------,1) = e
           10        10

          - 1397    - 1397
KummerU(---------,---------,1) = 
           10        10

             1397           1417                  1417
 1397*gamma(------)*(gamma(------)*e - kummerm(1,------,1))
              10             10                    10
------------------------------------------------------------
                                1417
                      10*gamma(------)
                                 10

          - 1397    - 1397   12      2/5  2
KummerM(---------,---------,----) = e   *e
           10        10      5

          - 1397    - 1397   12                  1397
KummerU(---------,---------,----) = (1397*gamma(------)*(
           10        10      5                    10
71746481373430634031294954664443705921549411424077607513961896135157303433516062796115875244140625
                    2/5  7/10        1417    2
                  *e   *5    *gamma(------)*e  - 
                                      10
24344700853849035700818673148074354758817652733157773392184531343019477693735336014107210586246213128985447429892804030005399393593757895097780327677952
                                                                          2/5
                                                                        *2

        7/10            1417   12
      *3    *kummerm(1,------,----)))/(
                         10    5
717464813734306340312949546644437059215494114240776075139618961351573034335160627961158752441406250
                     7/10        1417
                   *5    *gamma(------))
                                  10

          - 1397    - 1397    - 1397          1
KummerM(---------,---------,---------) = ------------
           10        10        10          7/10  139
                                          e    *e

          - 1397    - 1397    - 1397                  1397
KummerU(---------,---------,---------) = (1397*gamma(------)*( - 
           10        10        10                      10
212567495663303297519662433596963528677722951143732392822434307529861247918312684788866994674596144196868616065822748643411734186482425939893404665719527475329355936813211016172830688956933974043486859243594875896254908713306052460209605563066162704803073506155523685300835213856763052611669373327017337516100202429275776045541043302571869099957135889191233303801334553760006254341494325951532336811508595833526048489556116405666102486918801
                                           7/10          7/10
                                         *e    *( - 1397)

                  1417    - 1397    139
      *kummerm(1,------,---------)*e    + 
                   10      10
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
                                                                7/10
                                                             *10

              1417
      *gamma(------)))/(
               10
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
                                                                7/10   7/10
                                                              *e    *10

           1417    139
   *gamma(------)*e   )
            10


on rounded;


precision 30;


20

t!*k!*c := 7;


t*k*c := 7


%  To test each and every possible combination of
%  three arguments from t!*kummer!*b would take too
%  long, but we want the possibility of trying most
%  special cases.  Compromise: test every seventh
%  possibility.

for each a in t!*kummer!*b do
   for each b in t!*kummer!*b do
      for each z in t!*kummer!*b do
         << if t!*k!*c = 7
            then << write "KummerM(", a, ",", b, ",", z, ") = ",
                       kummerm(a,b,z);
                    write "KummerU(", a, ",", b, ",", z, ") = ",
                       kummeru(a,b,z);
                    t!*k!*c := 0 >>;
            t!*k!*c := t!*k!*c + 1 >>;


KummerM(0,0,0) = 1

KummerU(0,0,0) = kummeru(0,0,0)

KummerM(0,1,3.14159265358979323846264338328) = 1

KummerU(0,1,3.14159265358979323846264338328) = kummeru(0,1,

   3.14159265358979323846264338328)

KummerM(0,3.14159265358979323846264338328,26) = 1

KummerU(0,3.14159265358979323846264338328,26) = kummeru(0,

   3.14159265358979323846264338328,26)

KummerM(0,26,1) = 1

KummerU(0,26,1) = kummeru(0,26,1)

KummerM(1,0, - 3.14159265358979323846264338328) = kummerm(1,0,

    - 3.14159265358979323846264338328)

KummerU(1,0, - 3.14159265358979323846264338328) = kummeru(1,0,

    - 3.14159265358979323846264338328)

KummerM(1,3.14159265358979323846264338328,0) = 1

KummerU(1,3.14159265358979323846264338328,0) = kummeru(1,

   3.14159265358979323846264338328,0)

KummerM(1, - 3.14159265358979323846264338328,3.14159265358979323846264338328) = 

2692.89480079631357528203659153

KummerU(1, - 3.14159265358979323846264338328,3.14159265358979323846264338328) = 

0.129554194296952806409644905659

KummerM(1,26,26) = 7.74565667206271943920803547594

KummerU(1,26,26) = kummeru(1,26,26)

KummerM(3.14159265358979323846264338328,1,1) = 10.2259987795328570162092950355

KummerU(3.14159265358979323846264338328,1,1) = kummeru(

   3.14159265358979323846264338328,1,1)

KummerM(3.14159265358979323846264338328,3.14159265358979323846264338328,

 - 3.14159265358979323846264338328) = 0.0432139182637722497744177371717

KummerU(3.14159265358979323846264338328,3.14159265358979323846264338328,

 - 3.14159265358979323846264338328) = ( - 0.137891580772667438638357954721

                                        2.14159265358979323846264338328
   *( - 3.14159265358979323846264338328)

    + 1.22938452238615186004844111454)/

                                    2.14159265358979323846264338328
( - 3.14159265358979323846264338328)

KummerM(3.14159265358979323846264338328,26,0) = 1

KummerU(3.14159265358979323846264338328,26,0) = kummeru(

   3.14159265358979323846264338328,26,0)

KummerM( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328) = 

kummerm( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328)

KummerU( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328) = 

kummeru( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328)

KummerM( - 3.14159265358979323846264338328,1,26) = 6.185222265647228001735135594

62e+5

KummerU( - 3.14159265358979323846264338328,1,26) = kummeru(

    - 3.14159265358979323846264338328,1,26)

KummerM( - 3.14159265358979323846264338328, - 3.14159265358979323846264338328,1

) = 2.71828182845904523536028747135

KummerU( - 3.14159265358979323846264338328, - 3.14159265358979323846264338328,1

) = 19.2419564406028465661346237348

KummerM( - 3.14159265358979323846264338328,26, - 3.14159265358979323846264338328

) = 1.42892253084220157246185820464

KummerU( - 3.14159265358979323846264338328,26, - 3.14159265358979323846264338328

) = kummeru( - 3.14159265358979323846264338328,26,

             - 3.14159265358979323846264338328)

KummerM(26,1,0) = 1

KummerU(26,1,0) = kummeru(26,1,0)

KummerM(26,3.14159265358979323846264338328,3.14159265358979323846264338328) = 3.

91638029828702661403357541917e+5

KummerU(26,3.14159265358979323846264338328,3.14159265358979323846264338328) = 4.

18995913372628050180833640475e-32

KummerM(26, - 3.14159265358979323846264338328,26) = 2.19471945265322419268333614

674e+34

KummerU(26, - 3.14159265358979323846264338328,26) = 0


off rounded;


clear x, y, z, t!*k!*c;



df(df(kummerM(a,b,z),z),z);


                 2
(kummerm(2,3,z)*z  - 2*kummerm(2,3,z)*z + 2*kummerm(2,3,z) + 2*kummerm(1,3,z)*z

                                          2
  - 4*kummerm(1,3,z) + 2*kummerm(0,3,z))/z

df(kummerU(a,b,z),z);


 kummeru(2,3,z)*z - kummeru(2,3,z) - kummeru(1,3,z)
----------------------------------------------------
                         z


z := ((x^2 + y)^5) + (x^(x+y));


      x + y    10      8         6  2       4  3      2  4    5
z := x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y


df(df(kummerM(a,b,z),y),x);


  4*x + 4*y
(x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2      4*x + 4*y
 *log(x) *x + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

       4*x + 4*y
 *x + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

         3*x + 3*y
 *y + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  11       3*x + 3*y
 *log(x) *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  9         3*x + 3*y
 *log(x) *x *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  7  2       3*x + 3*y
 *log(x) *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  5  3       3*x + 3*y
 *log(x) *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  3  4      3*x + 3*y
 *log(x) *x *y  + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2    5    3*x + 3*y
 *log(x) *x*y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2        3*x + 3*y
 *log(x) *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11      3*x + 3*y
 *x   + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10         3*x + 3*y
 *x  *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10       3*x + 3*y
 *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9        3*x + 3*y
 *x *y + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9       3*x + 3*y
 *x  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  2       3*x + 3*y
 *x *y  + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8         3*x + 3*y
 *x *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  2       3*x + 3*y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7         3*x + 3*y
 *x *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  3       3*x + 3*y
 *x *y  + 60*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  2       3*x + 3*y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  3       3*x + 3*y
 *x *y  + 30*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  2       3*x + 3*y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  4       3*x + 3*y
 *x *y  + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  3       3*x + 3*y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  4       3*x + 3*y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  3       3*x + 3*y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  5       3*x + 3*y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  4      3*x + 3*y
 *x *y  + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     5      3*x + 3*y
 *x*y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     4    3*x + 3*y
 *x*y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

         3*x + 3*y
 *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6    3*x + 3*y
 *y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

         3*x + 3*y
 *y + 5*x

               x + y    10      8         6  2       4  3      2  4    5   9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 5

   3*x + 3*y
 *x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      3*x + 3*y
  20*x

               x + y    10      8         6  2       4  3      2  4    5   7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      3*x + 3*y
  20*x

               x + y    10      8         6  2       4  3      2  4    5   6  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       3*x + 3*y
 + 30*x

               x + y    10      8         6  2       4  3      2  4    5   5  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       3*x + 3*y
 + 30*x

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       3*x + 3*y
 + 20*x

               x + y    10      8         6  2       4  3      2  4    5   3  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       3*x + 3*y
 + 20*x

               x + y    10      8         6  2       4  3      2  4    5   2  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

      3*x + 3*y
 + 5*x

               x + y    10      8         6  2       4  3      2  4    5     4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  +

     3*x + 3*y
  5*x

               x + y    10      8         6  2       4  3      2  4    5   5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y  + 

  3*x + 3*y
 x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y ) + 2

   3*x + 3*y
 *x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2        3*x + 3*y
 *log(x) *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

         3*x + 3*y
 *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

       2*x + 2*y
 *y + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  21       2*x + 2*y
 *log(x) *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  19         2*x + 2*y
 *log(x) *x  *y + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  17  2        2*x + 2*y
 *log(x) *x  *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  15  3        2*x + 2*y
 *log(x) *x  *y  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  13  4        2*x + 2*y
 *log(x) *x  *y  + 252*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  11  5        2*x + 2*y
 *log(x) *x  *y  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  9  6        2*x + 2*y
 *log(x) *x *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  7  7       2*x + 2*y
 *log(x) *x *y  + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  5  8       2*x + 2*y
 *log(x) *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  3  9    2*x + 2*y
 *log(x) *x *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2    10    2*x + 2*y
 *log(x) *x*y   + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2      2*x + 2*y
 *log(x) *x + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   21    2*x + 2*y
 *x   + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   20         2*x + 2*y
 *x  *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   20       2*x + 2*y
 *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   19         2*x + 2*y
 *x  *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   19       2*x + 2*y
 *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   18  2        2*x + 2*y
 *x  *y  + 180*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   18         2*x + 2*y
 *x  *y + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   17  2       2*x + 2*y
 *x  *y  + 90*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   17         2*x + 2*y
 *x  *y + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   16  3        2*x + 2*y
 *x  *y  + 720*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   16  2        2*x + 2*y
 *x  *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   15  3        2*x + 2*y
 *x  *y  + 360*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   15  2        2*x + 2*y
 *x  *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   14  4         2*x + 2*y
 *x  *y  + 1680*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   14  3        2*x + 2*y
 *x  *y  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   13  4        2*x + 2*y
 *x  *y  + 840*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   13  3        2*x + 2*y
 *x  *y  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   12  5         2*x + 2*y
 *x  *y  + 2520*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   12  4        2*x + 2*y
 *x  *y  + 252*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11  5         2*x + 2*y
 *x  *y  + 1260*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11  4        2*x + 2*y
 *x  *y  + 252*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10  6         2*x + 2*y
 *x  *y  + 2520*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10  5       2*x + 2*y
 *x  *y  - 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10        2*x + 2*y
 *x   + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9  6         2*x + 2*y
 *x *y  + 1260*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9  5       2*x + 2*y
 *x *y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9        2*x + 2*y
 *x  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  7         2*x + 2*y
 *x *y  + 1680*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  6       2*x + 2*y
 *x *y  - 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8          2*x + 2*y
 *x *y + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  7        2*x + 2*y
 *x *y  + 840*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  6       2*x + 2*y
 *x *y  - 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7          2*x + 2*y
 *x *y + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  8        2*x + 2*y
 *x *y  + 720*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  7        2*x + 2*y
 *x *y  - 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  2       2*x + 2*y
 *x *y  + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  8        2*x + 2*y
 *x *y  + 360*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  7       2*x + 2*y
 *x *y  - 60*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  2       2*x + 2*y
 *x *y  + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  9        2*x + 2*y
 *x *y  + 180*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  8       2*x + 2*y
 *x *y  - 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  3       2*x + 2*y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  9       2*x + 2*y
 *x *y  + 90*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  8       2*x + 2*y
 *x *y  - 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  3       2*x + 2*y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  10       2*x + 2*y
 *x *y   + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  9       2*x + 2*y
 *x *y  - 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  4    2*x + 2*y
 *x *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     10       2*x + 2*y
 *x*y   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     9       2*x + 2*y
 *x*y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     4    2*x + 2*y
 *x*y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

       2*x + 2*y
 *x + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11    2*x + 2*y
 *y   + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

          2*x + 2*y
 *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5   19
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

     2*x + 2*y
 10*x

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

       2*x + 2*y
 + 50*x

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

     2*x + 2*y
 90*x

               x + y    10      8         6  2       4  3      2  4    5   17
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

       2*x + 2*y
 + 90*x

               x + y    10      8         6  2       4  3      2  4    5   16  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         2*x + 2*y
  + 400*x

               x + y    10      8         6  2       4  3      2  4    5   16
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

        2*x + 2*y
 + 360*x

               x + y    10      8         6  2       4  3      2  4    5   15  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         2*x + 2*y
  + 360*x

               x + y    10      8         6  2       4  3      2  4    5   14  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          2*x + 2*y
  + 1400*x

               x + y    10      8         6  2       4  3      2  4    5   14  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         2*x + 2*y
  + 840*x

               x + y    10      8         6  2       4  3      2  4    5   13  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         2*x + 2*y
  + 840*x

               x + y    10      8         6  2       4  3      2  4    5   12  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          2*x + 2*y
  + 2800*x

               x + y    10      8         6  2       4  3      2  4    5   12  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          2*x + 2*y
  + 1260*x

               x + y    10      8         6  2       4  3      2  4    5   11  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          2*x + 2*y
  + 1260*x

               x + y    10      8         6  2       4  3      2  4    5   10  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          2*x + 2*y
  + 3500*x

               x + y    10      8         6  2       4  3      2  4    5   10  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

       2*x + 2*y
  + 2*x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

       2*x + 2*y
 1260*x

               x + y    10      8         6  2       4  3      2  4    5   9  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 - 10*x

               x + y    10      8         6  2       4  3      2  4    5   9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

       2*x + 2*y
 1260*x

               x + y    10      8         6  2       4  3      2  4    5   8  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

         2*x + 2*y
 + 2800*x

               x + y    10      8         6  2       4  3      2  4    5   8  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

      2*x + 2*y
 840*x

               x + y    10      8         6  2       4  3      2  4    5   7  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 - 40*x

               x + y    10      8         6  2       4  3      2  4    5   7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

       2*x + 2*y
  840*x

               x + y    10      8         6  2       4  3      2  4    5   6  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

         2*x + 2*y
 + 1400*x

               x + y    10      8         6  2       4  3      2  4    5   6  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 - 20*x

               x + y    10      8         6  2       4  3      2  4    5   6  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        2*x + 2*y
 + 120*x

               x + y    10      8         6  2       4  3      2  4    5   6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

       2*x + 2*y
  360*x

               x + y    10      8         6  2       4  3      2  4    5   5  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 - 60*x

               x + y    10      8         6  2       4  3      2  4    5   5  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        2*x + 2*y
 + 360*x

               x + y    10      8         6  2       4  3      2  4    5   4  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        2*x + 2*y
 + 400*x

               x + y    10      8         6  2       4  3      2  4    5   4  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 - 40*x

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        2*x + 2*y
 + 120*x

               x + y    10      8         6  2       4  3      2  4    5   4  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 90*x

               x + y    10      8         6  2       4  3      2  4    5   3  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 - 40*x

               x + y    10      8         6  2       4  3      2  4    5   3  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 90*x

               x + y    10      8         6  2       4  3      2  4    5   2  9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 50*x

               x + y    10      8         6  2       4  3      2  4    5   2  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 - 30*x

               x + y    10      8         6  2       4  3      2  4    5   2  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   2  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5     9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  -

      2*x + 2*y
  10*x

               x + y    10      8         6  2       4  3      2  4    5     4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  +

      2*x + 2*y
  10*x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y   - 

    2*x + 2*y
 8*x

               x + y    10      8         6  2       4  3      2  4    5   5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y  - 

  2*x + 2*y
 x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y ) + 2

   2*x + 2*y
 *x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  11       2*x + 2*y
 *log(x) *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  9         2*x + 2*y
 *log(x) *x *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  7  2       2*x + 2*y
 *log(x) *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  5  3       2*x + 2*y
 *log(x) *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  3  4      2*x + 2*y
 *log(x) *x *y  + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2    5      2*x + 2*y
 *log(x) *x*y  - 3*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2        2*x + 2*y
 *log(x) *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11      2*x + 2*y
 *x   + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10         2*x + 2*y
 *x  *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10       2*x + 2*y
 *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9         2*x + 2*y
 *x *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9       2*x + 2*y
 *x  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  2       2*x + 2*y
 *x *y  + 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8         2*x + 2*y
 *x *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  2       2*x + 2*y
 *x *y  + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7         2*x + 2*y
 *x *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  3        2*x + 2*y
 *x *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  2       2*x + 2*y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  3       2*x + 2*y
 *x *y  + 60*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  2       2*x + 2*y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  4       2*x + 2*y
 *x *y  + 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  3       2*x + 2*y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  4       2*x + 2*y
 *x *y  + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  3       2*x + 2*y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  5       2*x + 2*y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  4      2*x + 2*y
 *x *y  + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     5       2*x + 2*y
 *x*y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     4      2*x + 2*y
 *x*y  - 3*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

         2*x + 2*y
 *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6      2*x + 2*y
 *y  - 3*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

          2*x + 2*y
 *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5   9
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

     2*x + 2*y
 10*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      2*x + 2*y
  40*x

               x + y    10      8         6  2       4  3      2  4    5   7
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      2*x + 2*y
  40*x

               x + y    10      8         6  2       4  3      2  4    5   6  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 60*x

               x + y    10      8         6  2       4  3      2  4    5   5  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 60*x

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   3  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   2  4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       2*x + 2*y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5     4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  +

      2*x + 2*y
  10*x

               x + y    10      8         6  2       4  3      2  4    5   5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y  + 

  2*x + 2*y
 x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y ) + 2

   2*x + 2*y
 *x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2        2*x + 2*y
 *log(x) *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

         2*x + 2*y
 *x + 2*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

       x + y
 *y + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  21       x + y
 *log(x) *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  19         x + y
 *log(x) *x  *y + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  17  2        x + y
 *log(x) *x  *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  15  3        x + y
 *log(x) *x  *y  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  13  4        x + y
 *log(x) *x  *y  + 252*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  11  5    x + y
 *log(x) *x  *y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  11        x + y
 *log(x) *x   + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  9  6      x + y
 *log(x) *x *y  - 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  9          x + y
 *log(x) *x *y + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  7  7       x + y
 *log(x) *x *y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  7  2       x + y
 *log(x) *x *y  + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  5  8       x + y
 *log(x) *x *y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  5  3       x + y
 *log(x) *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  3  9      x + y
 *log(x) *x *y  - 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  3  4    x + y
 *log(x) *x *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2    10    x + y
 *log(x) *x*y   - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2    5       x + y
 *log(x) *x*y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   30      x + y
 *x   + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   29        x + y
 *x   + 140*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   28         x + y
 *x  *y + 70*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   27          x + y
 *x  *y + 910*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   26  2        x + y
 *x  *y  + 455*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   25  2         x + y
 *x  *y  + 3640*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   24  3         x + y
 *x  *y  + 1820*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   23  3          x + y
 *x  *y  + 10010*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   22  4         x + y
 *x  *y  + 5005*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   21  4    x + y
 *x  *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   21          x + y
 *x   + 20020*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   20  5    x + y
 *x  *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   20         x + y
 *x  *y - 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   20          x + y
 *x   + 10010*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   19  5       x + y
 *x  *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   19         x + y
 *x  *y - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   19          x + y
 *x   + 30030*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   18  6       x + y
 *x  *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   18  2        x + y
 *x  *y  - 180*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   18            x + y
 *x  *y + 15015*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   17  6       x + y
 *x  *y  + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   17  2       x + y
 *x  *y  - 90*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   17            x + y
 *x  *y + 34320*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   16  7       x + y
 *x  *y  + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   16  3        x + y
 *x  *y  - 720*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   16  2          x + y
 *x  *y  + 17160*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   15  7        x + y
 *x  *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   15  3        x + y
 *x  *y  - 360*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   15  2          x + y
 *x  *y  + 30030*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   14  8        x + y
 *x  *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   14  4         x + y
 *x  *y  - 1680*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   14  3          x + y
 *x  *y  + 15015*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   13  8        x + y
 *x  *y  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   13  4        x + y
 *x  *y  - 840*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   13  3          x + y
 *x  *y  + 20020*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   12  9        x + y
 *x  *y  + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   12  5         x + y
 *x  *y  - 2520*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   12  4          x + y
 *x  *y  + 10010*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11  9        x + y
 *x  *y  + 252*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11  5         x + y
 *x  *y  - 1260*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11  4    x + y
 *x  *y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11          x + y
 *x   + 10010*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10  10        x + y
 *x  *y   + 252*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10  6         x + y
 *x  *y  - 2520*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10  5    x + y
 *x  *y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10         x + y
 *x  *y + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10         x + y
 *x   + 5005*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9  10        x + y
 *x *y   + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9  6         x + y
 *x *y  - 1260*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9  5      x + y
 *x *y  - 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9         x + y
 *x *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9         x + y
 *x  + 3640*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  11        x + y
 *x *y   + 210*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  7         x + y
 *x *y  - 1680*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  6      x + y
 *x *y  - 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  2       x + y
 *x *y  + 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8           x + y
 *x *y + 1820*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  11        x + y
 *x *y   + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  7        x + y
 *x *y  - 840*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  6       x + y
 *x *y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  2       x + y
 *x *y  + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7          x + y
 *x *y + 910*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  12        x + y
 *x *y   + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  8        x + y
 *x *y  - 720*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  7       x + y
 *x *y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  3        x + y
 *x *y  + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  2        x + y
 *x *y  + 455*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  12       x + y
 *x *y   + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  8        x + y
 *x *y  - 360*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  7       x + y
 *x *y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  3       x + y
 *x *y  + 60*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  2        x + y
 *x *y  + 140*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  13       x + y
 *x *y   + 45*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  9        x + y
 *x *y  - 180*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  8       x + y
 *x *y  - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  4       x + y
 *x *y  + 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  3       x + y
 *x *y  + 70*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  13       x + y
 *x *y   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  9       x + y
 *x *y  - 90*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  8      x + y
 *x *y  - 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  4       x + y
 *x *y  + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  3       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  14       x + y
 *x *y   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  10       x + y
 *x *y   - 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  9      x + y
 *x *y  - 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  5       x + y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  4      x + y
 *x *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     14    x + y
 *x*y   + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     10       x + y
 *x*y   - 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     9    x + y
 *x*y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     5       x + y
 *x*y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     4    x + y
 *x*y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11    x + y
 *y   - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6      x + y
 *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5   29
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

    x + y
 5*x

               x + y    10      8         6  2       4  3      2  4    5   28
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

        x + y
 + 100*x

               x + y    10      8         6  2       4  3      2  4    5   28
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

     x + y
 70*x

               x + y    10      8         6  2       4  3      2  4    5   27
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

       x + y
 + 70*x

               x + y    10      8         6  2       4  3      2  4    5   26  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 1300*x

               x + y    10      8         6  2       4  3      2  4    5   26
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

        x + y
 + 455*x

               x + y    10      8         6  2       4  3      2  4    5   25  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  + 455*x

               x + y    10      8         6  2       4  3      2  4    5   24  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 7800*x

               x + y    10      8         6  2       4  3      2  4    5   24  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 1820*x

               x + y    10      8         6  2       4  3      2  4    5   23  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 1820*x

               x + y    10      8         6  2       4  3      2  4    5   22  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

           x + y
  + 28600*x

               x + y    10      8         6  2       4  3      2  4    5   22  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 5005*x

               x + y    10      8         6  2       4  3      2  4    5   21  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 5005*x

               x + y    10      8         6  2       4  3      2  4    5   20  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

           x + y
  + 71500*x

               x + y    10      8         6  2       4  3      2  4    5   20  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

     x + y
  + x

               x + y    10      8         6  2       4  3      2  4    5   20
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

        x + y
 10010*x

               x + y    10      8         6  2       4  3      2  4    5   19  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

        x + y
  - 10*x

               x + y    10      8         6  2       4  3      2  4    5   19
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

        x + y
 10010*x

               x + y    10      8         6  2       4  3      2  4    5   18  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

            x + y
  + 128700*x

               x + y    10      8         6  2       4  3      2  4    5   18  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

        x + y
  - 20*x

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

        x + y
 15015*x

               x + y    10      8         6  2       4  3      2  4    5   17  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

        x + y
  - 90*x

               x + y    10      8         6  2       4  3      2  4    5   17
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

          x + y
 + 15015*x

               x + y    10      8         6  2       4  3      2  4    5   16  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

            x + y
  + 171600*x

               x + y    10      8         6  2       4  3      2  4    5   16  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

        x + y
  - 45*x

               x + y    10      8         6  2       4  3      2  4    5   16  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  - 160*x

               x + y    10      8         6  2       4  3      2  4    5   16
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

          x + y
 + 17160*x

               x + y    10      8         6  2       4  3      2  4    5   15  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  - 360*x

               x + y    10      8         6  2       4  3      2  4    5   15  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

           x + y
  + 17160*x

               x + y    10      8         6  2       4  3      2  4    5   14  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

            x + y
  + 171600*x

               x + y    10      8         6  2       4  3      2  4    5   14  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  - 240*x

               x + y    10      8         6  2       4  3      2  4    5   14  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  - 560*x

               x + y    10      8         6  2       4  3      2  4    5   14  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

           x + y
  + 15015*x

               x + y    10      8         6  2       4  3      2  4    5   13  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  - 840*x

               x + y    10      8         6  2       4  3      2  4    5   13  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

           x + y
  + 15015*x

               x + y    10      8         6  2       4  3      2  4    5   12  9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

            x + y
  + 128700*x

               x + y    10      8         6  2       4  3      2  4    5   12  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  - 630*x

               x + y    10      8         6  2       4  3      2  4    5   12  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  - 1120*x

               x + y    10      8         6  2       4  3      2  4    5   12  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

           x + y
  + 10010*x

               x + y    10      8         6  2       4  3      2  4    5   11  9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  - 1260*x

               x + y    10      8         6  2       4  3      2  4    5   11  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

           x + y
  + 10010*x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   10          x + y
 *y   + 71500*x

               x + y    10      8         6  2       4  3      2  4    5   10  9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  - 1008*x

               x + y    10      8         6  2       4  3      2  4    5   10  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  - 1400*x

               x + y    10      8         6  2       4  3      2  4    5   10  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

     x + y
  - x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

       x + y
 5005*x

               x + y    10      8         6  2       4  3      2  4    5   9  10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

          x + y
  - 1260*x

               x + y    10      8         6  2       4  3      2  4    5   9  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5   9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

       x + y
 5005*x

               x + y    10      8         6  2       4  3      2  4    5   8  11
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

           x + y
  + 28600*x

               x + y    10      8         6  2       4  3      2  4    5   8  10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

          x + y
  - 1050*x

               x + y    10      8         6  2       4  3      2  4    5   8  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

         x + y
 - 1120*x

               x + y    10      8         6  2       4  3      2  4    5   8  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

      x + y
 + 5*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y -

      x + y
  40*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

       x + y
 1820*x

               x + y    10      8         6  2       4  3      2  4    5   7  11
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

         x + y
  - 840*x

               x + y    10      8         6  2       4  3      2  4    5   7  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

        x + y
  1820*x

               x + y    10      8         6  2       4  3      2  4    5   6  12
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

          x + y
  + 7800*x

               x + y    10      8         6  2       4  3      2  4    5   6  11
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

         x + y
  - 720*x

               x + y    10      8         6  2       4  3      2  4    5   6  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 - 560*x

               x + y    10      8         6  2       4  3      2  4    5   6  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 30*x

               x + y    10      8         6  2       4  3      2  4    5   6  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 - 120*x

               x + y    10      8         6  2       4  3      2  4    5   6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

       x + y
  455*x

               x + y    10      8         6  2       4  3      2  4    5   5  12
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

         x + y
  - 360*x

               x + y    10      8         6  2       4  3      2  4    5   5  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 60*x

               x + y    10      8         6  2       4  3      2  4    5   5  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 + 455*x

               x + y    10      8         6  2       4  3      2  4    5   4  13
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

          x + y
  + 1300*x

               x + y    10      8         6  2       4  3      2  4    5   4  12
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

         x + y
  - 315*x

               x + y    10      8         6  2       4  3      2  4    5   4  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 - 160*x

               x + y    10      8         6  2       4  3      2  4    5   4  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 50*x

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 - 120*x

               x + y    10      8         6  2       4  3      2  4    5   4  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 70*x

               x + y    10      8         6  2       4  3      2  4    5   3  13
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

        x + y
  - 90*x

               x + y    10      8         6  2       4  3      2  4    5   3  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   3  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 70*x

               x + y    10      8         6  2       4  3      2  4    5   2  14
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

         x + y
  + 100*x

               x + y    10      8         6  2       4  3      2  4    5   2  13
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

        x + y
  - 80*x

               x + y    10      8         6  2       4  3      2  4    5   2  9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 20*x

               x + y    10      8         6  2       4  3      2  4    5   2  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 35*x

               x + y    10      8         6  2       4  3      2  4    5   2  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 40*x

               x + y    10      8         6  2       4  3      2  4    5   2  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

      x + y
 + 5*x

               x + y    10      8         6  2       4  3      2  4    5     14
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y   

       x + y
 - 10*x

               x + y    10      8         6  2       4  3      2  4    5     9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  +

      x + y
  10*x

               x + y    10      8         6  2       4  3      2  4    5     4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  +

     x + y
  5*x

               x + y    10      8         6  2       4  3      2  4    5   15
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y   - 

    x + y
 9*x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y   + 

    x + y
 9*x

               x + y    10      8         6  2       4  3      2  4    5   5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y  + 

  x + y              x + y    10      8         6  2       4  3      2  4    5
 x     *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  11      x + y
 *log(x) *x   + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  9         x + y
 *log(x) *x *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  7  2       x + y
 *log(x) *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  5  3      x + y
 *log(x) *x *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2  3  4    x + y
 *log(x) *x *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

        2    5       x + y
 *log(x) *x*y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   20       x + y
 *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   19        x + y
 *x   + 180*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   18         x + y
 *x  *y + 90*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   17          x + y
 *x  *y + 720*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   16  2        x + y
 *x  *y  + 360*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   15  2         x + y
 *x  *y  + 1680*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   14  3        x + y
 *x  *y  + 840*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   13  3         x + y
 *x  *y  + 2520*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   12  4         x + y
 *x  *y  + 1260*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11  4    x + y
 *x  *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   11         x + y
 *x   + 2520*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10  5    x + y
 *x  *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10         x + y
 *x  *y - 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10         x + y
 *x   + 1260*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9  5      x + y
 *x *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9         x + y
 *x *y - 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9         x + y
 *x  + 1680*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  6      x + y
 *x *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8  2        x + y
 *x *y  - 160*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8          x + y
 *x *y + 840*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  6       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  2       x + y
 *x *y  - 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7          x + y
 *x *y + 720*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  7       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  3        x + y
 *x *y  - 240*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  2        x + y
 *x *y  + 360*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  7       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  3        x + y
 *x *y  - 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  2        x + y
 *x *y  + 180*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  8       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  4        x + y
 *x *y  - 160*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  3       x + y
 *x *y  + 90*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  8      x + y
 *x *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  4       x + y
 *x *y  - 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  3       x + y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  9      x + y
 *x *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  5       x + y
 *x *y  - 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  4       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     9    x + y
 *x*y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     5       x + y
 *x*y  - 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     4    x + y
 *x*y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6       x + y
 *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5   19
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

     x + y
 10*x

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

        x + y
 + 100*x

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

     x + y
 90*x

               x + y    10      8         6  2       4  3      2  4    5   17
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

       x + y
 + 90*x

               x + y    10      8         6  2       4  3      2  4    5   16  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  + 800*x

               x + y    10      8         6  2       4  3      2  4    5   16
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

        x + y
 + 360*x

               x + y    10      8         6  2       4  3      2  4    5   15  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  + 360*x

               x + y    10      8         6  2       4  3      2  4    5   14  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 2800*x

               x + y    10      8         6  2       4  3      2  4    5   14  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  + 840*x

               x + y    10      8         6  2       4  3      2  4    5   13  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

         x + y
  + 840*x

               x + y    10      8         6  2       4  3      2  4    5   12  4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 5600*x

               x + y    10      8         6  2       4  3      2  4    5   12  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 1260*x

               x + y    10      8         6  2       4  3      2  4    5   11  4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 1260*x

               x + y    10      8         6  2       4  3      2  4    5   10  5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

          x + y
  + 7000*x

               x + y    10      8         6  2       4  3      2  4    5   10  4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

     x + y
  + x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

       x + y
 1260*x

               x + y    10      8         6  2       4  3      2  4    5   9  5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 20*x

               x + y    10      8         6  2       4  3      2  4    5   9
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

       x + y
 1260*x

               x + y    10      8         6  2       4  3      2  4    5   8  6
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

         x + y
 + 5600*x

               x + y    10      8         6  2       4  3      2  4    5   8  5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 15*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      x + y
  40*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

      x + y
 840*x

               x + y    10      8         6  2       4  3      2  4    5   7  6
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 80*x

               x + y    10      8         6  2       4  3      2  4    5   7
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

       x + y
  840*x

               x + y    10      8         6  2       4  3      2  4    5   6  7
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

         x + y
 + 2800*x

               x + y    10      8         6  2       4  3      2  4    5   6  6
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 70*x

               x + y    10      8         6  2       4  3      2  4    5   6  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 + 120*x

               x + y    10      8         6  2       4  3      2  4    5   6
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

       x + y
  360*x

               x + y    10      8         6  2       4  3      2  4    5   5  7
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 - 120*x

               x + y    10      8         6  2       4  3      2  4    5   5  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 + 360*x

               x + y    10      8         6  2       4  3      2  4    5   4  8
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 + 800*x

               x + y    10      8         6  2       4  3      2  4    5   4  7
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 - 110*x

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 + 120*x

               x + y    10      8         6  2       4  3      2  4    5   4  2
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 90*x

               x + y    10      8         6  2       4  3      2  4    5   3  8
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 80*x

               x + y    10      8         6  2       4  3      2  4    5   3  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 90*x

               x + y    10      8         6  2       4  3      2  4    5   2  9
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

        x + y
 + 100*x

               x + y    10      8         6  2       4  3      2  4    5   2  8
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 - 75*x

               x + y    10      8         6  2       4  3      2  4    5   2  4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   2  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5     9
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  -

      x + y
  20*x

               x + y    10      8         6  2       4  3      2  4    5     4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  +

      x + y
  10*x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y   - 

     x + y
 19*x

               x + y    10      8         6  2       4  3      2  4    5   5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y  + 

     x + y
 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   10       x + y
 *x   + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9       x + y
 *x  + 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   8         x + y
 *x *y + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7          x + y
 *x *y + 120*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   6  2       x + y
 *x *y  + 60*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  2       x + y
 *x *y  + 80*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   4  3       x + y
 *x *y  + 40*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  3       x + y
 *x *y  + 20*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   2  4       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     4       x + y
 *x*y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5   9
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  + 

     x + y
 10*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      x + y
  40*x

               x + y    10      8         6  2       4  3      2  4    5   7
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      x + y
  40*x

               x + y    10      8         6  2       4  3      2  4    5   6  2
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 60*x

               x + y    10      8         6  2       4  3      2  4    5   5  2
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 60*x

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   3  3
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   2  4
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5     4
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  +

      x + y
  10*x

               x + y    10      8         6  2       4  3      2  4    5   5
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y  + 

                 x + y    10      8         6  2       4  3      2  4    5   38
 50*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   

                    x + y    10      8         6  2       4  3      2  4    5
 + 900*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   36
 *x  *y + 7650

               x + y    10      8         6  2       4  3      2  4    5   34  2
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 40800

               x + y    10      8         6  2       4  3      2  4    5   32  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 153000

               x + y    10      8         6  2       4  3      2  4    5   30  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 428400

               x + y    10      8         6  2       4  3      2  4    5   28  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                    x + y    10      8         6  2       4  3      2  4    5
  - 60*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   28
 *x   + 928200

               x + y    10      8         6  2       4  3      2  4    5   26  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                     x + y    10      8         6  2       4  3      2  4    5
  - 780*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   26
 *x  *y + 1591200

               x + y    10      8         6  2       4  3      2  4    5   24  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 4680*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   24  2
 *x  *y  + 2187900

               x + y    10      8         6  2       4  3      2  4    5   22  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  - 17160

               x + y    10      8         6  2       4  3      2  4    5   22  3
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 2431000

               x + y    10      8         6  2       4  3      2  4    5   20  9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  - 42900

               x + y    10      8         6  2       4  3      2  4    5   20  4
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 2187900

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   10
 *y   - 77220

               x + y    10      8         6  2       4  3      2  4    5   18  5
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                    x + y    10      8         6  2       4  3      2  4    5
  + 60*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   18
 *x   + 1591200

               x + y    10      8         6  2       4  3      2  4    5   16
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   11
 *y   - 102960

               x + y    10      8         6  2       4  3      2  4    5   16  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                     x + y    10      8         6  2       4  3      2  4    5
  + 480*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   16
 *x  *y + 928200

               x + y    10      8         6  2       4  3      2  4    5   14
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   12
 *y   - 102960

               x + y    10      8         6  2       4  3      2  4    5   14  7
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  + 1680*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   14  2
 *x  *y  + 428400

               x + y    10      8         6  2       4  3      2  4    5   12
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   13
 *y   - 77220

               x + y    10      8         6  2       4  3      2  4    5   12  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  + 3360*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   12  3
 *x  *y  + 153000

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   14
 *y   - 42900

               x + y    10      8         6  2       4  3      2  4    5   10  9
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  + 4200*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   10  4
 *x  *y  + 40800

               x + y    10      8         6  2       4  3      2  4    5   8  15
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

  - 17160

               x + y    10      8         6  2       4  3      2  4    5   8  10
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                      x + y    10      8         6  2       4  3      2  4    5
  + 3360*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   8  5
 *x *y  + 7650

               x + y    10      8         6  2       4  3      2  4    5   6  16
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 4680*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   6  11
 *x *y   + 1680

               x + y    10      8         6  2       4  3      2  4    5   6  6
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                    x + y    10      8         6  2       4  3      2  4    5
 + 900*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   4  17
 *x *y   - 780

               x + y    10      8         6  2       4  3      2  4    5   4  12
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                     x + y    10      8         6  2       4  3      2  4    5
  + 480*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   4  7
 *x *y  + 50

               x + y    10      8         6  2       4  3      2  4    5   2  18
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                    x + y    10      8         6  2       4  3      2  4    5
  - 60*kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   2  13
 *x *y   + 60

               x + y    10      8         6  2       4  3      2  4    5   2  8
 *kummerm(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                    x + y    10      8         6  2       4  3      2  4    5
 + 100*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   28
 *x   + 1300

               x + y    10      8         6  2       4  3      2  4    5   26
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

                     x + y    10      8         6  2       4  3      2  4    5
 + 7800*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   24  2
 *x  *y  + 28600

               x + y    10      8         6  2       4  3      2  4    5   22  3
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 71500

               x + y    10      8         6  2       4  3      2  4    5   20  4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 128700

               x + y    10      8         6  2       4  3      2  4    5   18  5
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                     x + y    10      8         6  2       4  3      2  4    5
  - 160*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   18
 *x   + 171600

               x + y    10      8         6  2       4  3      2  4    5   16  6
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 1280*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   16
 *x  *y + 171600

               x + y    10      8         6  2       4  3      2  4    5   14  7
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 4480*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   14  2
 *x  *y  + 128700

               x + y    10      8         6  2       4  3      2  4    5   12  8
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 8960*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   12  3
 *x  *y  + 71500

               x + y    10      8         6  2       4  3      2  4    5   10  9
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  - 11200

               x + y    10      8         6  2       4  3      2  4    5   10  4
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

  + 28600

               x + y    10      8         6  2       4  3      2  4    5   8  10
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 8960*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   8  5
 *x *y  + 7800

               x + y    10      8         6  2       4  3      2  4    5   6  11
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 4480*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   6  6
 *x *y  + 1300

               x + y    10      8         6  2       4  3      2  4    5   4  12
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                      x + y    10      8         6  2       4  3      2  4    5
  - 1280*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   4  7
 *x *y  + 100

               x + y    10      8         6  2       4  3      2  4    5   2  13
 *kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                     x + y    10      8         6  2       4  3      2  4    5
  - 160*kummerm(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   2  8
 *x *y  + 100

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

                  x + y    10      8         6  2       4  3      2  4    5   16
 800*kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

 *y + 2800

               x + y    10      8         6  2       4  3      2  4    5   14  2
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  + 5600*kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   12  3
 *x  *y  + 7000

               x + y    10      8         6  2       4  3      2  4    5   10  4
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  + 5600*kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   8  5
 *x *y  + 2800

               x + y    10      8         6  2       4  3      2  4    5   6  6
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                    x + y    10      8         6  2       4  3      2  4    5
 + 800*kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   4  7
 *x *y  + 100

               x + y    10      8         6  2       4  3      2  4    5   2  8
 *kummerm(0,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y )

      2*x + 2*y      x + y  10       x + y  8         x + y  6  2
/(x*(x          + 2*x     *x   + 10*x     *x *y + 20*x     *x *y

            x + y  4  3       x + y  2  4      x + y  5    20       18
      + 20*x     *x *y  + 10*x     *x *y  + 2*x     *y  + x   + 10*x  *y

            16  2        14  3        12  4        10  5        8  6        6  7
      + 45*x  *y  + 120*x  *y  + 210*x  *y  + 252*x  *y  + 210*x *y  + 120*x *y

            4  8       2  9    10
      + 45*x *y  + 10*x *y  + y  ))

df(kummerU(a,b,z),x);


  2*x + 2*y
(x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

       2*x + 2*y
 *x + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x + 

  2*x + 2*y
 x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y + 

  x + y              x + y    10      8         6  2       4  3      2  4    5
 x     *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

          11      x + y
 *log(x)*x   + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   9         x + y
 *x *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   7  2       x + y
 *x *y  + 10*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   5  3      x + y
 *x *y  + 5*x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

   3  4    x + y
 *x *y  + x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

     5    x + y
 *x*y  - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

       x + y
 *x + x

               x + y    10      8         6  2       4  3      2  4    5   11
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

  x + y              x + y    10      8         6  2       4  3      2  4    5
 x     *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   10         x + y
 *x  *y + 10*x

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   + 

    x + y
 5*x

               x + y    10      8         6  2       4  3      2  4    5   9
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

     x + y
  5*x

               x + y    10      8         6  2       4  3      2  4    5   8  2
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   8
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y +

      x + y
  10*x

               x + y    10      8         6  2       4  3      2  4    5   7  2
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5   6  3
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 60*x

               x + y    10      8         6  2       4  3      2  4    5   6  2
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5   5  3
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5   4  4
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 40*x

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

      x + y
 + 5*x

               x + y    10      8         6  2       4  3      2  4    5   3  4
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

      x + y
 + 5*x

               x + y    10      8         6  2       4  3      2  4    5   2  5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

       x + y
 + 10*x

               x + y    10      8         6  2       4  3      2  4    5   2  4
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

    x + y
 + x

               x + y    10      8         6  2       4  3      2  4    5     5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x*y  -

   x + y              x + y    10      8         6  2       4  3      2  4    5
  x     *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

       x + y
 *x + x

               x + y    10      8         6  2       4  3      2  4    5   6
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*y  - 

  x + y              x + y    10      8         6  2       4  3      2  4    5
 x     *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

       x + y
 *y - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*log(x)

       x + y
 *x - x

               x + y    10      8         6  2       4  3      2  4    5
 *kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x - 

  x + y              x + y    10      8         6  2       4  3      2  4    5
 x     *kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

                      x + y    10      8         6  2       4  3      2  4    5
 *y + 10*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   20
 *x   + 90

               x + y    10      8         6  2       4  3      2  4    5   18
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y 

                    x + y    10      8         6  2       4  3      2  4    5
 + 360*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   16  2
 *x  *y  + 840

               x + y    10      8         6  2       4  3      2  4    5   14  3
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                      x + y    10      8         6  2       4  3      2  4    5
  + 1260*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   12  4
 *x  *y  + 1260

               x + y    10      8         6  2       4  3      2  4    5   10  5
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x  *y

                    x + y    10      8         6  2       4  3      2  4    5
  - 10*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   10
 *x   + 840

               x + y    10      8         6  2       4  3      2  4    5   8  6
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                   x + y    10      8         6  2       4  3      2  4    5   8
 - 40*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

 *y + 360

               x + y    10      8         6  2       4  3      2  4    5   6  7
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                   x + y    10      8         6  2       4  3      2  4    5   6
 - 60*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   2
 *y  + 90

               x + y    10      8         6  2       4  3      2  4    5   4  8
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                   x + y    10      8         6  2       4  3      2  4    5   4
 - 40*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   3
 *y  + 10

               x + y    10      8         6  2       4  3      2  4    5   2  9
 *kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                   x + y    10      8         6  2       4  3      2  4    5   2
 - 10*kummeru(2,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   4
 *y  - 10

               x + y    10      8         6  2       4  3      2  4    5   10
 *kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x   - 

                 x + y    10      8         6  2       4  3      2  4    5   8
 40*kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y

                    x + y    10      8         6  2       4  3      2  4    5
  - 60*kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )

   6  2
 *x *y  - 40

               x + y    10      8         6  2       4  3      2  4    5   4  3
 *kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x *y  

                   x + y    10      8         6  2       4  3      2  4    5   2
 - 10*kummeru(1,3,x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y )*x

   4       x + y    10      8         6  2       4  3      2  4    5
 *y )/(x*(x      + x   + 5*x *y + 10*x *y  + 10*x *y  + 5*x *y  + y ))




% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

%     9. Bessel functions

% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=


%  Lengthy test of the Bessel functions.  This isn't even
%  remotely exhaustive of the special cases -- though a
%  real person with lots of time could no doubt come up
%  with a better lot of tests than this automated rubbish.
%  Again, compromise by only actually doing one in five or
%  nine.  If you want a really thorough test, you can
%  easily change this to get it; but it'll take hours to
%  run.

clear p, q;



hankel1(p,q);


hankel1(p,q)

r := df(ws,q);


      hankel1(p - 1,q)*q - hankel1(p,q)*p
r := -------------------------------------
                       q


on complex;



r;


 besselj(p - 1,q)*q - besselj(p,q)*p + i*bessely(p - 1,q)*q - i*bessely(p,q)*p
-------------------------------------------------------------------------------
                                       q

p:=3/8;


      3
p := ---
      8

r;


               - 5          3*pi                   - 5          3*pi
(8*i*besselj(------,q)*cos(------)*q + 8*besselj(------,q)*sin(------)*q
               8             8                     8             8

                  - 3                    5
  + 3*i*besselj(------,q) + 8*i*besselj(---,q)*q
                  8                      8

                 3          3*pi                3          3*pi
  - 3*i*besselj(---,q)*cos(------) - 3*besselj(---,q)*sin(------))/(8
                 8           8                  8           8

         3*pi
   *sin(------)*q)
          8

q := pi;


q := pi

r;


               - 5           3*pi                    - 5           3*pi
(8*i*besselj(------,pi)*cos(------)*pi + 8*besselj(------,pi)*sin(------)*pi
               8              8                      8              8

                  - 3                     5
  + 3*i*besselj(------,pi) + 8*i*besselj(---,pi)*pi
                  8                       8

                 3           3*pi                3           3*pi
  - 3*i*besselj(---,pi)*cos(------) - 3*besselj(---,pi)*sin(------))/(8
                 8            8                  8            8

         3*pi
   *sin(------)*pi)
          8


on rounded;


*** Domain mode complex changed to complex-rounded 


r;


 - 0.119366207318921501826662822529

*hankel1(0.375,3.14159265358979323846264338328)

 + hankel1( - 0.625,3.14159265358979323846264338328)


off complex, rounded;


*** Domain mode complex-rounded changed to rounded 


df(df(besselj(pp,qq)+rr * hankel1(pp*2,qq) *
      bessely(pp-qq,qq),qq),qq);


                      2
(besselj(pp - 2,qq)*qq  - 2*besselj(pp - 1,qq)*pp*qq + besselj(pp - 1,qq)*qq

                     2
  + besselj(pp,qq)*pp  + besselj(pp,qq)*pp

                                               2
  + bessely(pp - qq,qq)*hankel1(2*pp - 2,qq)*qq *rr

  - 4*bessely(pp - qq,qq)*hankel1(2*pp - 1,qq)*pp*qq*rr

  + bessely(pp - qq,qq)*hankel1(2*pp - 1,qq)*qq*rr

                                             2
  + 4*bessely(pp - qq,qq)*hankel1(2*pp,qq)*pp *rr

  + 2*bessely(pp - qq,qq)*hankel1(2*pp,qq)*pp*rr

                                                    2
  + df(bessely(pp - qq,qq),qq,2)*hankel1(2*pp,qq)*qq *rr

                                                        2
  + 2*df(bessely(pp - qq,qq),qq)*hankel1(2*pp - 1,qq)*qq *rr

                                                              2
  - 4*df(bessely(pp - qq,qq),qq)*hankel1(2*pp,qq)*pp*qq*rr)/qq


% Possible values for real args
t!*bes!*vr := { 1, pi, -pi, 26 }$



% Possible values for real and imaginary parts of complex args
t!*bes!*vc := { 0, 3, -41/2 }$



array s!*bes(4)$



s!*bes(1) := "BesselJ"$


s!*bes(2) := "BesselY"$


s!*bes(3) := "BesselI"$


s!*bes(4) := "BesselK"$



pre := 16;


pre := 16

precision pre;


30

preord := 10**pre;


preord := 10000000000000000

t!*b!*c := 3;


t*b*c := 3


algebraic procedure do!*one!*bessel(s,n,z);
   (if s = 1 then besselj(n,z)
      else if s = 2 then bessely(n,z)
      else if s = 3 then besseli(n,z)
      else besselk(n,z));


do*one*bessel


algebraic procedure pr!*bessel(s,n,z,k);
   << if t!*b!*c = k
      then
         << on rounded;
            bes1 := do!*one!*bessel(s,n,z);
            precision(pre+5);
            bes2 := do!*one!*bessel(s,n,z);
            if bes1 neq 0
               then disc := floor abs(100*(bes2-bes1)*preord/bes1)
               else disc := 0;
            precision pre;
            write s!*bes(s), "(", n, ",", z, ") = ", bes1;
            if not numberp disc then
               << precom := !*complex;
                  on complex;
                  disc := disc;
                  if not precom then off complex >>;
            if disc neq 0
               then write "   (discrepancy ", disc, "% of one s.f.)";
            if numberp disc and disc > 200 then
               << write "***** WARNING  Significant Inaccuracy.";
                  write "      Lower  precision result:";
                  write "      ", bes1;
                  write "      Higher precision result:";
                  precision(pre+5); write "      ", bes2; precision pre >>;
            off rounded;
            t!*b!*c := 0 >>;
      t!*b!*c := t!*b!*c + 1 >>;


pr*bessel


%  About to begin Bessel test.  We have a list of possible
%  values, and we test every Bessel, with every value on the
%  list as both order and argument.  Every Bessel is computed
%  twice, to different precisions (differing by 3), and any
%  discrepancy is reported.  The value reported is the diff-
%  erence between the two computed values, expressed as a
%  percentage of the unit of the least significant displayed
%  digit.  A discrepancy between 100% and 200% means that the
%  last digit of the displayed value was found to differ at
%  higher precision; values greater than 200% are cause for
%  concern.  An ideal discrepancy would be between about 1%
%  and 20%; if the value is found to be zero, no discrepancy
%  is reported.

off msg;



for s := 1:4 do
   << write(" ... Testing ", s!*bes(s), " for real domains ... ");
      for each n in t!*bes!*vr do
         for each z in t!*bes!*vr do
            pr!*bessel(s, n, z, 5) >>;


 ... Testing BesselJ for real domains ... 

BesselJ(1, - 3.141592653589793) =  - 0.2846153431797528

BesselJ(3.141592653589793,26) =  - 0.006989220174690161

   (discrepancy 5% of one s.f.)

BesselJ(26,1) = 3.660826744416803e-35

 ... Testing BesselY for real domains ... 

BesselY(1,3.141592653589793) = 0.358872916776719

BesselY(3.141592653589793, - 3.141592653589793) = 

                                          6.283185307179586
 0.1545613960392598*( - 1.570796326794897)                  - 4.829362563540275
--------------------------------------------------------------------------------
                                          3.141592653589793
                    ( - 1.570796326794897)

BesselY( - 3.141592653589793,26) =  - 0.1386083623177915

 ... Testing BesselI for real domains ... 

BesselI(1,1) = 0.565159103992485

BesselI(3.141592653589793,3.141592653589793) = 1.011423335928613

BesselI( - 3.141592653589793, - 3.141592653589793) =  - 0.8856101155917482

 + 0.4221616153281286*i

BesselI(26,26) = 68397.86776155122

 ... Testing BesselK for real domains ... 

BesselK(3.141592653589793,1) = 9.025908765806763

BesselK( - 3.141592653589793,3.141592653589793) = 0.1107526602738113

   (discrepancy 1% of one s.f.)

BesselK(26, - 3.141592653589793) = besselk(26, - 3.141592653589793)


on complex;



for s := 1:3 do
   << write (" ... Testing  ", s!*bes(s), " for complex domains ... ");
      for each nr in t!*bes!*vc do
         for each ni in t!*bes!*vc do
            for each zr in t!*bes!*vc do
               for each zi in t!*bes!*vc do
                  pr!*bessel(s, nr+ni*i, zr+zi*i, 9) >>;


 ... Testing  BesselJ for complex domains ... 

BesselJ(0, - 20.5 + 3.0*i) = 1.05389016561334 + 1.410918160335249*i

BesselJ(3*i, - 20.5 + 3.0*i) = 0.01225787392170983 + 0.01066256817009466*i

BesselJ( - 20.5*i, - 20.5 + 3.0*i) =  - 6.607837931625446e+38

 + 7.203284455482089e+38*i

BesselJ(3, - 20.5 + 3.0*i) = 1.568613483726435 - 0.7011991107137573*i

BesselJ(3 + 3*i, - 20.5 + 3.0*i) = 0.007904103001381543 - 0.006566520928092784*i

BesselJ(3.0 - 20.5*i, - 20.5 + 3.0*i) =  - 7.069920310202644e+37

 - 1.753271554229047e+37*i

BesselJ( - 20.5, - 20.5 + 3.0*i) = 0.1758742246345278 - 0.332739860634916*i

BesselJ( - 20.5 + 3.0*i, - 20.5 + 3.0*i) = 0.08815299110072903

 - 0.1369698556512304*i

BesselJ( - 20.5 - 20.5*i, - 20.5 + 3.0*i) =  - 5.364748129151297e+46

 + 2.608178375230083e+47*i

 ... Testing  BesselY for complex domains ... 

BesselY(0, - 20.5 + 3.0*i) =  - 1.404746667469566 + 1.060048452645186*i

BesselY(3*i, - 20.5 + 3.0*i) = 0.4973091982659732 + 0.7985114801567726*i

BesselY( - 20.5*i, - 20.5 + 3.0*i) =  - 7.203284455482089e+38

 - 6.607837931625446e+38*i

   (discrepancy 10% of one s.f.)

BesselY(3, - 20.5 + 3.0*i) = 0.6963128100601111 + 1.576222640523309*i

BesselY(3 + 3*i, - 20.5 + 3.0*i) =  - 1.117333163968302 + 0.9789575771194796*i

BesselY(3.0 - 20.5*i, - 20.5 + 3.0*i) = 1.753271554229047e+37

 - 7.069920310202644e+37*i

BesselY( - 20.5, - 20.5 + 3.0*i) = 0.2353954565395826 + 0.144691313932682*i

BesselY( - 20.5 + 3.0*i, - 20.5 + 3.0*i) =  - 0.1527215881543493

 + 0.2371137974094512*i

BesselY( - 20.5 - 20.5*i, - 20.5 + 3.0*i) =  - 2.608178375230083e+47

 - 5.364748129151297e+46*i

 ... Testing  BesselI for complex domains ... 

BesselI(0, - 20.5 + 3.0*i) =  - 6.891185608459107e+7 - 1.506065792318474e+7*i

BesselI(3*i, - 20.5 + 3.0*i) =  - 6879.511500081906 - 1745.250262122384*i

BesselI( - 20.5*i, - 20.5 + 3.0*i) = 4.756052726395977e+40

 - 1.836844915663626e+40*i

BesselI(3, - 20.5 + 3.0*i) = 5.56813934269752e+7 + 1.026348768124686e+7*i

BesselI(3 + 3*i, - 20.5 + 3.0*i) = 5917.619873410601 - 1360.623977225443*i

BesselI(3.0 - 20.5*i, - 20.5 + 3.0*i) = 1.125266362182384e+40

 - 3.487618645712341e+39*i

BesselI( - 20.5, - 20.5 + 3.0*i) =  - 0.0005935206748136158

 - 0.001045512507192035*i

BesselI( - 20.5 + 3.0*i, - 20.5 + 3.0*i) = 0.0001367212493519011

 - 0.00008899048591346719*i

BesselI( - 20.5 - 20.5*i, - 20.5 + 3.0*i) =  - 4.705541285798881e+45

 + 6.968045629188714e+45*i


off complex;



on msg;



write (" ...");


 ...

write ("Bessel test complete.");


Bessel test complete.


end;
(TIME:  specfn 121310 136641)