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Thread: Help!!!! Stirling's formula!!!!

  1. #1
    Mar 2013

    Help!!!! Stirling's formula!!!!

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

    Using Stirling's formula show that( see the first attached file stirling1!!!), 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 attached file stirling2).
    Is this equal to the result i have to show??

    Thank you!!!!

    Attached Thumbnails Attached Thumbnails Help!!!! Stirling's formula!!!!-stirling2-1-.png   Help!!!! Stirling's formula!!!!-stirling1-.png  
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