A Sonine-Gegenbauer Integral of the Neumann Function

Motivated by a desire to express in closed form a certain potential occurring in the study of diffraction of a plane electromagnetic wave by a wedge, Miller and Exton developed computable expressions for a large class of Sonine-Gegenbauer type integrals. In the present paper one of these integrals, given previously in terms of generalized hypergeometric functions in three variables, is now obtained in terms of hypergeometric functions in two variables, thereby much reducing the complexity of the representation. In the course of this investigation certain identities involving Srivastava’s F 3.-function, Kamp´e de F´eriet functions, and Wright functions are deduced. In addition, evaluations of integrals of Bessel functions related to the above analysis are provided