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Assuming I have a Gamma distributed random Variable $x \sim Gamma( \alpha, \beta )$. Now I like to have the following two expectation values (integrals):

  1. $E \left[ x \ln x \right]$
  2. $E \left[ \ln \Gamma \left( x \right) \right]$ with $\Gamma \left( x \right)$ being the Gamma function

Many thanks in advance

  • 0
    At least at first glance, the second integral seems quite complicated, considering the expressions for the Log Gamma Function (see, for example, http://mathworld.wolfram.com/LogGammaFunction.html).2011-02-10

2 Answers 2