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Gamma Function Using Spouge's Method
08-21-2015, 09:48 AM
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RE: Gamma Function Using Spouge's Methjod
(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 But there is also the unpublished work of Paul Godfrey, discussed by Viktor Toth on his old http://www.rskey.org website, that reports a matrix algebra method of generating the Lanczos formula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.

"To live or die by your own sword one must first learn to wield it aptly."
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RE: Gamma Function Using Spouge's Methjod - Ángel Martin - 08-21-2015 09:48 AM



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