1234567891011121314151617181920212223242526 |
- #!/usr/bin/ruby
- # The derivatives ζ'(−2n) at trivial zeros.
- define π = Num.pi
- func zeta_derivative_trivial_zero(n) {
- (-1)**n * zeta(2*n + 1) * ((2*n)!) / 2**(2*n + 1) / π**(2*n)
- }
- each(1..10, {|n|
- say "zeta'(#{'%3s' % -2*n}) =~ #{zeta_derivative_trivial_zero(n)}"
- })
- __END__
- zeta'( -2) =~ -0.030448457058393270780251530471154776647000483545
- zeta'( -4) =~ 0.0079838114502686242806966707987893039052376933623
- zeta'( -6) =~ -0.00589975914351593745062987740839202557980153462016
- zeta'( -8) =~ 0.00831616198560224735952442651053421422567412291883
- zeta'(-10) =~ -0.0189299263381403742289805022903467952319852580952
- zeta'(-12) =~ 0.0632705833414630005951823012343077675114181847532
- zeta'(-14) =~ -0.291657724743873520321224003070250666970263038533
- zeta'(-16) =~ 1.77302566089909639624778734418929448135541982765
- zeta'(-18) =~ -13.7427682502140544352205641905185510730953721577
- zeta'(-20) =~ 132.28099750421251452709821158578551868064801
|