Logarithmic Integrals, Polylogarithmic Integrals and Euler sums
Bernard J. Laurenzi
TL;DR
This paper explores the relationships among integrals involving logarithms, polylogarithms, and Euler sums, using Nielsen's generalized polylogarithms as a unifying framework to reveal new connections.
Contribution
It introduces Nielsen's generalized polylogarithms to unify and analyze relations among various logarithmic and polylogarithmic integrals and Euler sums.
Findings
Derived new relations among logarithmic and polylogarithmic integrals
Unified various Euler sums using Nielsen's generalized polylogarithms
Provided a comprehensive framework for analyzing polylogarithmic integrals
Abstract
Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical functions and polynomials