Extended Reaction Rate Integral as Solutions of Some General Differential Equations

TL;DR

This paper introduces an extended reaction rate integral for nonresonant thermonuclear reactions, linking it to special functions and differential equations, with implications for nonextensive statistical mechanics.

Contribution

It presents a novel approach to evaluate extended reaction rate integrals using special functions and derives the differential equations they satisfy.

Findings

Extended integrals expressed in terms of special functions.

Derived differential equations for the extended integrals.

Discussed limiting cases and their implications.

Abstract

Here an extended form of the reaction rate probability integral, in the case of nonresonant thermonuclear reactions with the depleted tail and the right tail cut off, is considered. The reaction rate integral then can be looked upon as the inverse of the convolution of the Mellin transforms of Tsallis type statistics of nonextensive statistical mechanics and stretched exponential as well as that of superstatistics and stretched exponentials. The differential equations satisfied by the extended probability integrals are derived. The idea used is a novel one of evaluating the extended integrals in terms of some special functions and then by invoking the differential equations satisfied by these special functions. Some special cases of limiting situations are also discussed.