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## Re: [Bug-gsl] bug: gsl_sf_bessel_zero_Jnu(double nu, unsigned int s)

**From**: |
Gerard Jungman |

**Subject**: |
Re: [Bug-gsl] bug: gsl_sf_bessel_zero_Jnu(double nu, unsigned int s) |

**Date**: |
08 May 2003 15:34:15 -0600 |

On Thu, 2003-05-08 at 14:44, Brian Gough wrote:
>* Michael Gilbert writes:*
>* > Hi,*
>* > *
>* > If nu is negative, gsl_sf_bessel_zero_Jnu(nu, s) returns an error. This *
>* > is a trivial because Jnu(-x, s) = Jnu(x, s), so to handle the issue i *
>* > just do gsl_sf_bessel_zero_Jnu(fabs(x), s). I think this would be an *
>* > easy bug to fix.*
J(-nu,x) != J(nu,x)
If nu is an integer, then J(-n,x) = (-1)^n J(n,x). If nu is not
an integer, the relation is less simple, involving Hankel functions.
In fact, it is known that complex zeroes occur for non-integral nu,
when nu < -1.
As I say in the code, it is possible to do. But if it were
simple, I would have done it.
It might be a good idea for me to add a function
gsl_sf_bessel_zero_Jn(int n, unsigned int s), for integer
order. The usefulness would have to be balanced against
the extra cruft.
>* Thanks for the bug report. I found the following comment in*
>* the source code bessel_zero.c:*
>* *
>* else if(nu < 0.0) {*
>* /* This can be done, I'm just lazy now. */*
>* result->val = 0.0;*
>* result->err = 0.0;*
>* GSL_ERROR("unimplemented", GSL_EUNIMPL);*
>* }*
>* *
>* Until there is an implementation I will update the*
>* documentation to say that negative nu is not supported.*
It is not clear what it would mean to support it, given that
complex zeroes occur.
--
Gerard Jungman <address@hidden>
Los Alamos National Laboratory