On the Mellin transform of products of Bessel and generalized hypergeometric functions

We deduce in an elementary way representations for the Mellin transform of a product of Bessel functions 0F1[−a2x2] and generalized hypergeometric functions pFp+1[−b2x2] for a,b>0. As a corollary we obtain a transformation formula for p+1Fp[1] which was discovered by Wimp in 1987 by using Baileyʹs method for the specialization 3F2[1].