Gosper's Verstion of Stirling's Formula

Date: 05/30/2002 at 07:01:20
From: Amy Choi
Subject: Stirling's formula

I am doing a project on Stirling's formula, and I found that 
there is a better approximation to n! which was noted by Gosper.

I would like to know a proof of the approximation which is
     
            n! ˜ sqrt((2n + 1/3)Pi) * n^n * exp(-n)

Thank you.

Date: 05/30/2002 at 09:38:29
From: Doctor Mitteldorf
Subject: Re: Stirling's formula

The derivation comes from expressing the log of the factorial as 
the sum of n logs, then noticing that, for large n, this looks 
like the Riemann sum for the corresponding integral of log(n).  

There's a fuller explanation at 

  http://mathworld.wolfram.com/StirlingsApproximation.html

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

Date: 06/01/2002 at 02:38:25
From: Amy Choi
Subject: Thank you (Stirling's formula)

Thank you for answering my question. That was very helpful.