Gamma Function Using Spouge's Method

[Ángel Martin]

(08-20-2015 07:49 PM)lcwright1964 Wrote:  

(08-19-2015 08:56 PM)Ángel Martin Wrote:  Yes I used 13-digit routines for the MCODE version in the SandMath, which uses the Lanczos formula

May I ask which coefficients? Lanczos offers some in his original paper, and I believe that rendering is quoted in Numerical Recipes verbatim. But there is also the unpublished work of Paul Godfrey, discussed by Viktor Toth on his old http://www.rskey.org website, that reports a matrix algebra method of generating the Lanczos formula coefficients. I think I observed years ago that Godfrey's reported errors in a Matlab implementation were somewhat overly optimistic, as he only seemed to test his formulae with integral and half-integral arguments.

Indeed it was the formula with the coefficients published on Viktor's page. You can also see it in the SandMath manual - the most recent version is available at TOS, search for SandMath - and an older version is available here:
http://systemyde.com/pdf/SANDMATH-44_3x3_Manual.pdf

Incidentally I also implemented the same approach on the 41Z module using complex math routines - not 13-digit accurate unfortunately but still holding very nicely given the task to perform. It is an ALL-MCODE version as well.

Thanks for sharing the link to Dr. Pugh's work, very enjoyable.