Transforming an equation with logarithms

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  • Thread starter Pnin
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  • #1
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I want to approximate the logarithm of the Binomial coefficient log (n!/ ((n - m)! m!) with the the Stirling approximation log x! ≈ x log x - x

I got

n log n - m log m - (n - m) log(n - m)

but I want

(n - m) log (n/(n - m)) + m log (n/m)

Can someone help how to transform the first equation into the latter?
 

Answers and Replies

  • #2
Gaussian97
Homework Helper
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Try to add and subtract ##m \log{n}## in your first expresion
 
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Likes Pnin and mfb
  • #3
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thanks!
 

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