Gamma Function Division

Date: 12/20/2005 at 08:53:05
From: Vinicius
Subject: Gamma Function Division

Is there any formula for Gamma(n)/Gamma(m) for n and m integer values
>= 1 and m < n?

Gamma(n) can be too big, and I need a result with an |absolute error|
<= 1.  Stirling's Approximation doesn't apply.  I already have the
Gamma(n) formula.  But I need some formula to get Gamma(n)/Gamma(m)
directly without two integrals.  I suppose I could write a computer
program to do the calculation with exact value.

Date: 12/20/2005 at 10:03:32
From: Doctor George
Subject: Re: Gamma Function Division

Hi Vinicius,

Thanks for writing to Doctor Math.

You should consider using logarithms and computing

   ln(gamma(n)/gamma(m)) = ln(gamma(n)) - ln(gamma(m))

The logarithm of the gamma function is sometimes called the log-gamma
function and it has been studied extensively. See this link:

  Log Gamma Function
    http://mathworld.wolfram.com/LogGammaFunction.html 

Here is one place where you can find code for the log-gamma function:

    http://www.moshier.net/#Cephes 

Does that make sense? Write again if you need more help.

- Doctor George, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 12/21/2005 at 11:16:43
From: Vinicius
Subject: Thank you (Gamma Function Division)

That makes great sense.  Thanks!