Re: Formula Stirlinga
- To: mathgroup at smc.vnet.net
- Subject: [mg130696] Re: Formula Stirlinga
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Fri, 3 May 2013 03:51:49 -0400 (EDT)
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- Delivered-to: l-mathgroup@wolfram.com
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- References: <20130502014311.555F56A80@smc.vnet.net>
It works fine in the ratio form. The difference form appears to be
numerically unstable unless you use Log.
$Version
"9.0 for Mac OS X x86 (64-bit) (January 24, 2013)"
Clear[n];
Limit[
n!/(Sqrt[2*Pi*n]*(n/E)^n),
n -> Infinity]
1
With[{n = 1000},
N[n!/(Sqrt[2*Pi*n]*(n/E)^n)]]
1.00008
Limit[
Log[n!] - Log[Sqrt[2*Pi*n]*(n/E)^n],
n -> Infinity]
0
With[{n = 1000},
N[Log[n!] - Log[Sqrt[2*Pi*n]*(n/E)^n]]]
0.0000833333
Bob Hanlon
On Wed, May 1, 2013 at 9:43 PM, <karchevskymi at gmail.com> wrote:
> n = 1000;
> N[n! - Sqrt[2*Pi*n]*(n/Exp[1])^n] = 3.35308734163*10^2563
> Why does Stirling's formula works incorrect?
>
>
- References:
- Formula Stirlinga
- From: karchevskymi@gmail.com
- Formula Stirlinga