From: dmoews@xraysgi.ims.uconn.edu (David Moews)
Subject: Re: gamma function for a computer ...
Date: 12 Jan 2001 13:13:21 -0800
Newsgroups: sci.math
Summary: Stirling's formula for log(gamma(z))

In article <120120010909400540%edgar@math.ohio-state.edu>,
G. A. Edgar <edgar@math.ohio-state.edu> wrote:
|How about this.  Use Stirling's formula for large enough x
|(how large, depends on the number of correct digits you want),
|then use the functional equation for smalleer x (reduce it
|1 at a time)...?

This is the approach Pari uses.  (Why not use Pari, or some other package?)
For the benefit of the original poster, I will state Stirling's formula.  It is

log gamma(z) = (z-1/2) log z - z + 1/2 log(2pi)
                   + sum(z^{1-2m} B_{2m}/(2m(2m-1)), m=1, ..., n)
                   + R,

where for z>0, |R|, the absolute value of the remainder term, is bounded by
z^{-1-2n} |B_{2n+2}|/((2n+1)(2n+2)).  B_{q} is the qth Bernoulli number,
which is the coefficient of t^q in t/(e^t-1).  Note that this is for 
log gamma(z).  Exponentiate to get gamma(z).
-- 
David Moews                                       dmoews@xraysgi.ims.uconn.edu