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The gamma function

  1. Nov 26, 2004 #1
    The definition of this function is
    Gamma(z) = integral(0, inf)(t^(z-1)e^(-t) dt)

    Well, I can't understand what the t stands for. The only parameter is z... Is it an arbitrary number?
     
  2. jcsd
  3. Nov 26, 2004 #2

    arildno

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    Your integrand is a function of TWO variables:
    [tex]f(z,t)=t^{z-1}e^{-t}[/tex]
    When you integrate f(z,t) over the t-domain, ([tex]0\leq{t}<\infty[/tex]) , what you are left with, is a function of z alone:
    [tex]\Gamma(z)=\int_{0}^{\infty}f(z,t)dt[/tex]
     
  4. Nov 29, 2004 #3
    I think I get it. Thanks.
     
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