Fourier transform representation of the generalized hypergeometric functions with applications to the confluent and Gauss hypergeometric functions

We present a Fourier transform representation of the generalized hypergeometric functions. We then use this representation to evaluate integrals of products of two generalized hypergeometric functions. A number of integral identities for confluent and Gauss hypergeometric functions are presented. The results for Euler’s gamma function are deduced as special cases.