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May we have a similar approximation for lower incomplete gamma function $\gamma(s,x)$, as we have a Stirling's approximation for Gamma function $\Gamma(s)$.

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    $\begingroup$ Did you try Laplace's method? $\endgroup$ – Siméon Aug 26 '14 at 12:35
  • $\begingroup$ I did try a Laplace method, and I came up with the same Stirling aprrox. as we have for $\Gamma(x)$, because Laplace method don't care about the limits of integral. And lower gamma incomplete function is only different from gamma function in limits. By the way, your advice of using Laplace method was useful ! $\endgroup$ – kaka Aug 27 '14 at 0:42

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