ON HYPERGEOMETRIC SERIES REDUCTIONS FROM INTEGRAL REPRESENTATIONS, THE KAMPÉ DE FÉRIET FUNCTION AND ELSEWHERE

Abstract

Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrödinger equation or in the summation of perturbation expansions in quantum mechanics. For these applications, it is of interest to obtain analytic expressions, and we present the reduction of a number of cases of pFp and p+1Fp, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.