Memory issue

[Marc Glisse]

On Thu, 23 Dec 2010, Craig Helfgott wrote:

> As it turns out, it was not a memory leak issue.  Instead, the issue was
> that my complex gamma function algorithm was a memory-hog when the imaginary
> part of the argument got large.  I'm still trying to figure out why.
>
> I'm not fond of Spouge's approximation -- too many sqrts and powers of e for
> me.  I had been using
>
> Gamma(z) ~= N^z e^{-N} / z \sum_{j=0}^{4N} N^j / (z+1)...(z+j) + E(N,z)
>
> for 1 <= Re(z) <= 2, with E(N,z) < 2^{-N}.  But this requires 10 times as
> many terms as Spouge's approximation (and like I said my implementation has
> some problems).
>
> Does anyone have a gamma approximation/algorithm that they prefer, and why?

mpfr uses Spouge, so it can't be that bad...
http://www.mpfr.org/algo.html

Specialists for this kind of computation are more likely to be found on 
the mpfr mailing-list.

-- 
Marc Glisse