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Math Help - Integral Question

  1. #1
    VkL
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    Integral Question



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  2. #2
    o_O
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  3. #3
    MHF Contributor matheagle's Avatar
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    That's the definition of the Gamma function...

    \Gamma (a)=\int_0^{\infty} t^{a-1} e^{-t} dt.

    for a>0. The first thing you learn about this function is that

    \Gamma (a)=(a-1)\Gamma (a-1) and it's easy to show that

    \Gamma (1)=1. Thus \Gamma (2)=1...., whence \Gamma (n)=(n-1)! where n is an integer.
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