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- /* specfunc/gegenbauer.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 3 of the License, or (at
- * your option) any later version.
- *
- * This program is distributed in the hope that it will be useful, but
- * WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
- */
- /* Author: G. Jungman */
- #include "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_gegenbauer.h"
- #include "gsl_specfunc__error.h"
- /* See: [Thompson, Atlas for Computing Mathematical Functions] */
- int
- gsl_sf_gegenpoly_1_e(double lambda, double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(lambda == 0.0) {
- result->val = 2.0*x;
- result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_SUCCESS;
- }
- else {
- result->val = 2.0*lambda*x;
- result->err = 4.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_SUCCESS;
- }
- }
- int
- gsl_sf_gegenpoly_2_e(double lambda, double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(lambda == 0.0) {
- const double txx = 2.0*x*x;
- result->val = -1.0 + txx;
- result->err = 2.0 * GSL_DBL_EPSILON * fabs(txx);
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_SUCCESS;
- }
- else {
- result->val = lambda*(-1.0 + 2.0*(1.0+lambda)*x*x);
- result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(lambda));
- return GSL_SUCCESS;
- }
- }
- int
- gsl_sf_gegenpoly_3_e(double lambda, double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(lambda == 0.0) {
- result->val = x*(-2.0 + 4.0/3.0*x*x);
- result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(x));
- return GSL_SUCCESS;
- }
- else {
- double c = 4.0 + lambda*(6.0 + 2.0*lambda);
- result->val = 2.0*lambda * x * ( -1.0 - lambda + c*x*x/3.0 );
- result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(lambda * x));
- return GSL_SUCCESS;
- }
- }
- int
- gsl_sf_gegenpoly_n_e(int n, double lambda, double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(lambda <= -0.5 || n < 0) {
- DOMAIN_ERROR(result);
- }
- else if(n == 0) {
- result->val = 1.0;
- result->err = 0.0;
- return GSL_SUCCESS;
- }
- else if(n == 1) {
- return gsl_sf_gegenpoly_1_e(lambda, x, result);
- }
- else if(n == 2) {
- return gsl_sf_gegenpoly_2_e(lambda, x, result);
- }
- else if(n == 3) {
- return gsl_sf_gegenpoly_3_e(lambda, x, result);
- }
- else {
- if(lambda == 0.0 && (x >= -1.0 || x <= 1.0)) {
- /* 2 T_n(x)/n */
- const double z = n * acos(x);
- result->val = 2.0 * cos(z) / n;
- result->err = 2.0 * GSL_DBL_EPSILON * fabs(z * result->val);
- return GSL_SUCCESS;
- }
- else {
- int k;
- gsl_sf_result g2;
- gsl_sf_result g3;
- int stat_g2 = gsl_sf_gegenpoly_2_e(lambda, x, &g2);
- int stat_g3 = gsl_sf_gegenpoly_3_e(lambda, x, &g3);
- int stat_g = GSL_ERROR_SELECT_2(stat_g2, stat_g3);
- double gkm2 = g2.val;
- double gkm1 = g3.val;
- double gk = 0.0;
- for(k=4; k<=n; k++) {
- gk = (2.0*(k+lambda-1.0)*x*gkm1 - (k+2.0*lambda-2.0)*gkm2) / k;
- gkm2 = gkm1;
- gkm1 = gk;
- }
- result->val = gk;
- result->err = 2.0 * GSL_DBL_EPSILON * 0.5 * n * fabs(gk);
- return stat_g;
- }
- }
- }
- int
- gsl_sf_gegenpoly_array(int nmax, double lambda, double x, double * result_array)
- {
- int k;
- /* CHECK_POINTER(result_array) */
- if(lambda <= -0.5 || nmax < 0) {
- GSL_ERROR("domain error", GSL_EDOM);
- }
- /* n == 0 */
- result_array[0] = 1.0;
- if(nmax == 0) return GSL_SUCCESS;
- /* n == 1 */
- if(lambda == 0.0)
- result_array[1] = 2.0*x;
- else
- result_array[1] = 2.0*lambda*x;
- /* n <= nmax */
- for(k=2; k<=nmax; k++) {
- double term1 = 2.0*(k+lambda-1.0) * x * result_array[k-1];
- double term2 = (k+2.0*lambda-2.0) * result_array[k-2];
- result_array[k] = (term1 - term2) / k;
- }
-
- return GSL_SUCCESS;
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_gegenpoly_1(double lambda, double x)
- {
- EVAL_RESULT(gsl_sf_gegenpoly_1_e(lambda, x, &result));
- }
- double gsl_sf_gegenpoly_2(double lambda, double x)
- {
- EVAL_RESULT(gsl_sf_gegenpoly_2_e(lambda, x, &result));
- }
- double gsl_sf_gegenpoly_3(double lambda, double x)
- {
- EVAL_RESULT(gsl_sf_gegenpoly_3_e(lambda, x, &result));
- }
- double gsl_sf_gegenpoly_n(int n, double lambda, double x)
- {
- EVAL_RESULT(gsl_sf_gegenpoly_n_e(n, lambda, x, &result));
- }
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