Math Is Fun Forum

mathmari

Member

Registered: 2013-03-31

Posts: 2

Stirling's formula

Hello!!! Could anyone help me to solve this exercise?

Using Stirling's formula show that( see the first uploaded image), where S(x)=-xlnx-(1-x)ln(1-x), 0<=x<=1.
I used n!=e^(-n)n^(n+1/2)(2π)^(1/2)*(1+O(1/n)) and my result is (see the second uploaded image).
Is this equal to the result i have to show??

Thank you!!!!

Last edited by mathmari (2013-03-31 08:09:48)

stapel

Member

Registered: 2006-07-22

Posts: 15

Re: Stirling's formula

For other users, the images contain the following:

...and: