The Mellin transform of a product of two hypergeometric functions

摘要

We give an overview of known properties of the Mellin transform F(s) of the product of generalized hypergeometric functions _0F_1[- a~2x~2]_1F_2[- b~2x~2] for a > 0 and b > 0. In particular, we derive a new representation for F(s) that is valid in both the critical and supercritical cases where a = b.