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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.

annales polonici mathematici

Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions