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I'm new here and hope you can help.

It's really late here in South Africa, maybe my mind just doesn't want to function now! But I need to figure out how to get a closed form expression hopefully for $E(\ln X)$ and even $E(\ln (X^2))$ if $X$ is $\Gamma(a,b)$ distributed. Any help would be greatly appreciated!!

Scrofungulus

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    Is it $E(\ln (X^2))$ or $E(\ln^2 (X))$ ?2012-04-28
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    $\ln (X^2)$ is the same as $2\ln(X)$, so its expected value is just $2$ times that of $\ln X$. If you meant $(\ln X)^2$, that should be written differently.2012-04-29
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    [Wikipedia says](http://en.wikipedia.org/wiki/Gamma_distribution), and Maple confirms, that $E(\ln X) = -\ln b + \psi(a)$, where $\psi(t) = \frac{d}{dt} \ln \Gamma(t)$ is the digamma function.2012-04-29
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    @NateEldredge Should be E(lnX)=lnb+ψ(a)2018-03-23
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    @yliueagle: I think there is a difference of notational conventions. Compared with the definition in user26872's answer, Wikipedia replaces $b$ with $1/b$, which accounts for the sign difference.2018-03-23
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    @NateEldredge Then I see it2018-03-24

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