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Evaluating integral in terms of Gamma functions

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data

    The Gamma function is given by [itex]\Gamma[/itex](x) = 0 tx-1e-t dt

    Evaluate 0 exp(-αy2)dy in terms of Gamma functions.

    2. Relevant equations


    3. The attempt at a solution

    Honestly, I don't know where to start. I have knowledge of parametric differentiation (we use alpha as the variable in class which may hint at its usage here) but I don't immediately see how it would help or what it even means to evaluate the integral "in terms of gamma functions."

    I'm not just looking for the answer, I'd like a starting hint or tip to get going.
  2. jcsd
  3. Feb 29, 2012 #2

    Ray Vickson

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    You obviously need to find some alternative expression for the Gamma function that involves an integration with exp(-y^2) in it.

    Last edited: Feb 29, 2012
  4. Feb 29, 2012 #3


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    I think arex can work with that definition. Try the change of variable x=ay^2.
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