On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere

TL;DR

This paper develops methods to reduce complex hypergeometric series to simpler forms, facilitating their use in quantum mechanics, statistical physics, and chemistry by providing explicit analytic expressions.

Contribution

It introduces new reduction techniques for hypergeometric series pFp and p+1Fp, mainly for p=2 and p=3, enhancing their applicability in physical sciences.

Findings

Derived explicit reductions for specific hypergeometric series

Improved analytic expressions for series solutions in quantum mechanics

Enhanced tools for applications in physics and chemistry

Abstract

Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrodinger 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+1F_p, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.