A Sonine-Gegenbauer integral of the Neumann function (Q1917655)

The author deals with the Sonine-Gegenbauer type integral whose integrands contain Bessel functions \(J\nu\) and \(Y\nu\). It is shown that the integrals in question can be expressed in terms of the hypergeometric functions of two variables (Eq. (3.7)). Some interesting identities for the bivariate hypergeometric functions are derived. An integral representation for the Wright function \(W\) is also included.