Gosper's Verstion of Stirling's FormulaDate: 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. |
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