Infinite integrals in terms of series

TL;DR

This paper derives and evaluates infinite integrals involving generalized logarithms and polynomials, expressing them as finite series with special functions, and explores special cases involving fundamental constants.

Contribution

The work introduces new formulas for infinite integrals involving generalized logarithms, expressed via finite series with Hurwitz-Lerch zeta functions, including special cases.

Findings

Integrals expressed in terms of Hurwitz-Lerch zeta functions

Special cases related to fundamental constants

Explicit formulas for integrals involving generalized logarithms

Abstract

In this work we derive and evaluate some infinite integrals involving the product of a generalized logarithm and polynomial functions in the denominator. These integrals are expressed in terms of finite series involving the Hurwitz-Lerch zeta function. We produce special cases of these integrals in terms of other special functions and fundamental constants.