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



integral of a rational function (1+a_i s)^-1/prod((1+a_j s)^k)
This looks very much like a Lauricella Hypergeometric function: <http://en.wikipedia.org/wiki/Lauricella_hypergeometric_series>


