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### 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)

```
Associated Topics:
College Number Theory

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