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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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