Re: [Help-gsl] complex numbers and zeta function

[Tommy Nordgren]

On 16 jun 2008, at 23.08, Jordi Gutiérrez Hermoso wrote:

> On 16/06/2008, Ruben Henner Zilibowitz <address@hidden>  
> wrote:
> > Has there been any thought given to implementations of the zeta  
> > function and
> > eta function for complex numbers, instead of just for reals?
>
> I don't know if any thought has been given to it until now, but you're
> right that it doesn't seem to be implemented. I looked around, and I
> saw it in Pari ($PARI_SOURCE_PATH/src/basemath/trans3.c) and there's
> also a very simple-minded implementation in Octave-forge in the
> special function package.
>
> I trust the Pari implementation more. Perhaps you would like to read
> through it and implement it for the GSL.
>
> Abramowitz and Stegun also have some useful formulae in section 23.2
> (if you have a hard time finding this reference, I can provide it for
> you). I quickly glanced at it, and it looks like Pari uses the Euler
> product to compute zeta(s) for complex s.
>
> HTH,
> - Jordi G. H.

	Abramowitz & Stegun, Handbook of Mathematical Functions, is available  
from
Dover Publications with ISBN 0486612724
----------------------------------
Skinheads are so tired of immigration, that they are going to move to  
a country that don't accept immigrants!
Tommy Nordgren
address@hidden