Fox’s <i>H</i>-Functions: A Gentle Introduction to Astrophysical Thermonuclear Functions

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 largely distinct velocity distributions, namely the Maxwell–Boltzmann distribution, the pathway distribution, and the Mittag-Leffler distribution. Moreover, a natural generalization of the Maxwell–Boltzmann velocity distribution is discussed. Furthermore, an explicit evaluation of the reaction rate integral in the high-energy cut-off case is carried out. Generalized special functions of mathematical physics like Meijer’s G-function and Fox’s H-functions and their utilization in mathematical physics are the prime focus of this paper.

Keywords

• reaction rate probability integral
• astrophysical thermonuclear functions
• Fox’s H-function
• incomplete H-function
• Mittag-Leffler function
• Maxwell–Boltzmann distribution