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Re: [Bug-gsl] Bessel Jnu domain error

From: Gerard Jungman
Subject: Re: [Bug-gsl] Bessel Jnu domain error
Date: Tue, 22 May 2012 14:21:47 -0600
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:11.0) Gecko/20120329 Thunderbird/11.0.1

On 05/18/2012 10:43 AM, Jonathan Taylor wrote:
In the documentation, there are no specifications for the values of nu in
the evaluation of bessel_Jnu. However after running the command for nu<  0,
a domain error was shot at me. After looking at the source code, it indeed
shows that a domain error is thrown when nu<  0.
I wasn't entirely sure from your message whether you know the relationship between 
nu>0 and nu<0, but for Bessel functions of the first kind there is a very 
simple relationship - see
http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html equation 51.

For non-integer nu, J(nu,x) and J(-nu,x) are not related by the above formula, rather there is an imaginary part proportional to sin(nu x) Y(nu,x). It can be obtained easily
from Abramowitz+Stegun 9.1.3, 9.1.4, and 9.1.6.

If you happen to want integer values of nu, use the bessel_Jn functions
rather than bessel_Jnu.

G. Jungman

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