Stirling's Approximation

Date: 05/16/2001 at 01:28:08
From: faith
Subject: Factorials

My dad and I are trying to figure out if there is a way to get the 
answer to a factorial without having to multiply out all the numbers.

Date: 05/16/2001 at 11:42:07
From: Doctor Rob
Subject: Re: Factorials

Thanks for writing to Ask Dr. Math, Faith.

If you need all the digits, there is no better way. If you just need 
an approximate answer, there is Stirling's Approximation:

   sqrt(2*Pi*n)*(n/e)^n <= n! <= sqrt(2*Pi*n)*(n/e)^n*(1+1/[12*n-1])

where Pi = 3.14159265 and e = 2.71828183, approximately.

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