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Is there any closed-form expression for the following integral:

$\int_0^\infty \frac{1}{(1+a_i s) \prod_{j=1}^n (1+a_j s)^k} ds $

where the ai are >0 and k is a positive integer. And, if k is not an integer?

Thank you

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Is this meant to be a correction of… or a separate question? If the former, then please in the future edit the original question instead of reposting it. – Emil Jeřábek Jan 19 '12 at 15:00
up vote 1 down vote accepted

This looks very much like a Lauricella Hypergeometric function:

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