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Gamma and Beta Integrals

  1. Jun 23, 2011 #1
    1. The problem statement, all variables and given/known data

    The Gamma and Beta integrals are defined respectively as

    [tex]\Gamma (z) = \int^{\infty}_0 t^{z-1} e^{-t}\;dt[/tex]
    [tex]B(p,q) = \int^1_0 t^{p-1} (1-t)^{q-1}\;dt.[/tex]
    Determine for what values of the complex parameters z, p, q the integrals converge absolutely and explain why.

    3. The attempt at a solution

    How would I do this? Is the answer: [tex]\text{Re}(z) > 0,\;p,\,q>0\;?[/tex]
    If so, how do I show it and explain why?
     
    Last edited: Jun 23, 2011
  2. jcsd
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