On the Mellin transform of products of Bessel and generalized hypergeometric functions (Q1375449)

The author derives in an elementary way representations for the Mellin transform of a product of Bessel functions \({_0F_1}(- a^2x^2)\) and generalized hypergeometric functions \({_pF_{p+1}}(- b^2x^2)\), \(a,b>0\). Preparing the calculations an asymptotic expansion of \({_pF_{p+1}}(-z^2)\) as \(z\to\infty\), \(|\arg(z)|< \pi/2\) is derived, which is essential for the calculations.