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Find upper limit of improper integral - Numerical Integration

  1. Feb 26, 2012 #1
    Find upper limit of improper integral -- Numerical Integration

    Hi,

    I have the following complicated integral willing to integrate numerically. The integral is:

    [itex] \int _0^{\infty }x\frac{\beta^\alpha}{\Gamma(\alpha)}x^{-\alpha-1}e^{-\beta/x}dx [/itex].

    We know that the integral converges to:
    [itex] ((1/\beta)^\alpha \beta^{\alpha+1})/(\alpha-1)[/itex].

    Can anyone suggest a methodology of deriving the upper bound of the limit of this integral for numerical evaluation purposes?

    Thanks for your time.

    BR,

    Alex
     
  2. jcsd
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