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Asymptotic behavior of this function?

  1. Aug 7, 2014 #1
    Hi

    How to estimate the asymptotic behavior of this function?

    [tex]f(x)=\sum_{k=1}^{x}\log(k)[/tex]
    I mean, a closed form function g(x) such that f(x)/g(x) tends to 1 as x goes to infinity.
     
  2. jcsd
  3. Aug 7, 2014 #2

    pasmith

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    Homework Helper

    x is an integer, yes? Then [itex]f(x) = \log(x!)[/itex]. The standard asymptotic approximation for the factorial function is Stirling's approximation.
     
  4. Aug 7, 2014 #3
    Haha, exactly what I was looking for. Thanks!
     
  5. Aug 8, 2014 #4
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