Re: Formula Stirlinga
- To: mathgroup at smc.vnet.net
- Subject: [mg130705] Re: Formula Stirlinga
- From: Bill Rowe <readnews at sbcglobal.net>
- Date: Sat, 4 May 2013 03:17:41 -0400 (EDT)
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On 5/1/13 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? Stirling's formula is a valid approximation. But the way you are trying to demonstrate that isn't effective. Note In[1]:= n = 1000; N[(Sqrt[2*Pi*n]*(n/E)^n)/n!] Out[2]= 0.999917 In[3]:= 100 (1 - %) Out[3]= 0.00833299 That is there is an error of about 0.008% and In[4]:= Log[10, n!] + Log[10, %/100] Out[4]= 2563.53 That is an error of 0.008 amounts to a difference of 10^2563