Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2013-04-01 07:09:03

mathmari
Novice

Online

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!!!!


Uploaded Images
View Image: stirling1!!!.png View Image: stirling2.png    

Last edited by mathmari (2013-04-01 07:09:48)

#2 2013-04-01 22:35:33

stapel
Member

Offline

Re: Stirling's formula

For other users, the images contain the following:

...and:

Board footer

Powered by FluxBB