A family of polylogarithmic integrals

TL;DR

This paper studies a class of integrals arising in statistical plasma physics, providing closed-form solutions using special functions, which enhances understanding of their mathematical structure and potential applications.

Contribution

It introduces a comprehensive analysis of polylogarithmic integrals from plasma physics, deriving closed-form expressions with special functions.

Findings

Closed-form representations of integrals involving parameters.

Connection of integrals to special functions.

Potential applications in plasma physics and related fields.

Abstract

In this paper we investigate a class of integrals that were encountered in the course of a work on statistical plasma physics, in the so-called Sommerfeld temperature-expansion of the electronic entropy. We show that such integrals, involving some parameters, can be fully described in closed form represented by special functions.