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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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  • 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?
>
>



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