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Math Help - How to take the derivative of the following function

  1. #1
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    How to take the derivative of the following function

    Hi this is the function:

    G(a) = integral from 0 to infinity of [t^(a-1)*e^-t*dt]

    What is G'(a)?

    Thanks =D
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  2. #2
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    Quote Originally Posted by feiyingx View Post
    Hi this is the function:

    G(a) = integral from 0 to infinity of [t^(a-1)*e^-t*dt]

    What is G'(a)?

    Thanks =D
    Say a>0 then,

    L{ t^(a-1) } = Gamma(a)/s^a

    Note, your function is the Laplace transform evaluated at 1.
    Thus,
    G(a) = Gamma(a)/1^a = Gamma(a)

    The derivative of the gamma function is.
    The Psi(x)*Gamma(x)
    Where "psi" is the Digamma function.
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