Fox's H-Functions: A Gentle Introduction Through Astrophysical Thermonuclear Functions

TL;DR

This paper provides a comprehensive introduction to Fox's H-functions by applying them to evaluate thermonuclear reaction rates across different velocity distributions relevant to astrophysics.

Contribution

It introduces the use of Fox's H-function and Meijer G-function for analytic evaluation of thermonuclear reaction rates in astrophysics.

Findings

Analytic expressions for reaction rates using Fox's H-function.

Comparison of Maxwell-Boltzmann, pathway, and Mittag-Leffer distributions.

Demonstrates the utility of special functions in astrophysical calculations.

Abstract

Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three distinct velocity distributions, namely the Maxwell-Boltzmann distribution, the pathway distribution, and the Mittag-Leffer distribution. We emphasize the utilization of Meijer G-function and Fox H-function which are special functions of mathematical physics.