Re: [Bug-gsl] Bessel Jnu domain error

[Gerard Jungman]

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