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Re: Formula Stirlinga
Posted:
May 4, 2013 4:22 PM


On 5/1/13 at 9:43 PM, karchevskymi@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



