Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions
We evaluate an integral involving an Hermite polynomial, a generalized hypergeometric series and Fox's H-function, and employ it to evaluate a double integral involving Hermite polynomials, generalized hypergeometric series and the H-function. We further utilize the integral to establish a Fourier-Hermite expansion and a double Fourier-Hermite expansion for products of generalized hypergeometric functions.