I am having trouble with calculating the following integral: $$ \int_{0}^{\infty} \ln{(1 + \alpha x)\, G^{k,0}_{k,k}\left[e^{-x}\left|^{(a_k)}_{(b_k)} \right. \right]} \, dx, $$ where $\alpha > 0$ and $G^{m,n}_{p,q}[\cdot | \cdot]$ is the Meijer-G function. Any ideas or references would be very helpful. Thank you!
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$\begingroup$ Have you asked Mathematica or Maple? $\endgroup$– Neil StricklandDec 12, 2014 at 13:03
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$\begingroup$ Maple does not even do the $G^{1,0}_{1,1}$ case, where the G can be evaluated in closed form first. $\endgroup$– Gerald EdgarDec 12, 2014 at 22:10
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