Looking for Borwein's/Zucker's fast algorithm for the gamma function.

AI Thread Summary
The Borwein/Zucker algorithm for computing the gamma function is noted for its efficiency, utilizing arithmetic-geometric mean (AGM) and elliptic integrals for rapid high-precision calculations. Users are struggling to find the algorithm online, with one participant expressing a need for just the algorithm rather than the entire paper, which is behind a paywall. Another user offers to share a PDF of the paper if it is acceptable. Additional resources, such as a related discussion on Math Stack Exchange, are suggested for further insights. The conversation reflects a collaborative effort to access and understand this complex mathematical algorithm.
mesa
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I have heard that the Borwein/Zucker algorithm for computing certain values of the gamma function is pretty awesome, but finding it online is proving elusive...

Does anyone know the algorithm?
 
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BOAS said:
Is this what you're looking for?

http://imajna.oxfordjournals.org/content/12/4/519

That is as far as I have gotten (can't afford the $38). I don't need the whole paper, although it would be nice to have just the algorithm would be good enough for now.

As I understand it they use AGM and elliptic integrals of the first kind in order to compute large decimal approximations for certain values of the gamma function with very few steps, but that is about all I know of it so far :P
 
mesa said:
That is as far as I have gotten (can't afford the $38). I don't need the whole paper, although it would be nice to have just the algorithm would be good enough for now.

As I understand it they use AGM and elliptic integrals of the first kind in order to compute large decimal approximations for certain values of the gamma function with very few steps, but that is about all I know of it so far :P

I have access to it, and if it's not objectionable to you, I'm happy to email you a pdf.

Did you see this discussion?

http://math.stackexchange.com/quest...-gamma-function-to-high-precision-efficiently

I have literally no idea what they're talking about, but perhaps they discuss it in enough detail for you.
 
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