Is there any closedform 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
Is there any closedform 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 


This looks very much like a Lauricella Hypergeometric function: http://en.wikipedia.org/wiki/Lauricella_hypergeometric_series 

