A versatile integral in physics and astronomy

TL;DR

This paper introduces a versatile integral connecting various integrals in physics and astronomy, with representations using advanced special functions, unifying multiple concepts across disciplines.

Contribution

It presents a general integral framework linking diverse integrals in physics, astronomy, and statistics, with representations via Meijer's G and Fox's H functions.

Findings

Unified integral representation for multiple physics and astronomy integrals

Connections to special functions like Meijer's G and Fox's H functions

Applicable to reaction rates, distributions, and statistical mechanics

Abstract

This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in astronomy and physics. Reaction rate probability integrals in the theory of nuclear reaction rates, Kr\"atzel integrals in applied analysis, inverse Gaussian distribution, generalized type-1, type-2 and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck-Cohen superstatistics in statistical mechanics and the general pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of generalized special functions such as Meijer's G-function and Fox's H-function are also pointed out.