On the definite integral of two confluent hypergeometric functions related to the Kampé de Fériet double series

Abstract

The Kampé de Fériet double series $F_{1:1;1}^{1:1;1}$ is studied through the solution to the associated first-order nonhomogeneous differential equation. It is shown that the integral of $t^{\beta +l}M(\cdot ;\beta ;\lambda t)M(\cdot ;\beta ;-\lambda t)$ over $t\in [0,T]$, $T\ge 0$, $l=0,1,\dots$, $\Re \beta +l>-1$, is a linear combination of functions $F_{1:1;1}^{1:1;1}$. The integral is a generalization of a class of so-called Coulomb integrals involving regular Coulomb wave functions.

14 pages, accepted for publication in Lith Math J

References in corpus (2)

• Integrals containing confluent hypergeometric functions with applications to perturbed singular potentials
• Identities between Appell's and hypergeometric functions