The Mellin transform of a product of two hypergeometric functions

We give an overview of known properties of the Mellin transform F(s) of the product of generalized hypergeometric functions 0F1[−a2x2] 1F2[−b2x2] 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.