integral of a rational function (1+a_i s)^-1/prod((1+a_j s)^k)

Question

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

Is this meant to be a correction of http://mathoverflow.net/questions/86101/integral-of-a-rational-function-1a-i-s-prod1a-j-sk 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

score 1 · Accepted Answer · answered Jan 19 '12 at 14:44

1

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

answered Jan 19 '12 at 14:44

Igor Rivin

1 Answers1