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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

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