Some Double Integrals Stemming from the Boltzmann Equation in the Kinetic Theory of Gasses

Abstract

The main object of this article is to revisit a certain double integral involving Kummer’s confluent hypergeometric function 1F1 , which arose in the study of the collision terms of the celebrated Boltzmann equation in the kinetic theory of gases. Here, in this article, we propose to investigate some novel extensions and generalizations of this family of double integrals. We also point out some relevant connections of the results, which are presented here, with other related recent developments in the theory and applications of hypergeometric functions.