Integrals containing confluent hypergeometric functions with applications to perturbed singular potentials

TL;DR

This paper derives a unified approach to evaluate integrals involving confluent hypergeometric functions using Appell's F_2 series, with applications to singular potentials in quantum mechanics.

Contribution

It introduces a method to compute integrals of confluent hypergeometric functions via a single formula involving Appell's F_2 series, simplifying complex integral evaluations.

Findings

Unified integral formula for confluent hypergeometric functions

Techniques for computing Appell's F_2 series

Applications to matrix elements in quantum potentials

Abstract

We show that many integrals containing products of confluent hypergeometric functions follow directly from one single integral that has a very simple formula in terms of Appell's double series F_2. We present some techniques for computing such series. Applications requiring the matrix elements of singular potentials and the perturbed Kratzer potential are presented.