Integrals of polylogarithms and infinite series involving generalized harmonic numbers
Rusen Li
TL;DR
This paper provides explicit evaluations of infinite series involving generalized harmonic numbers and derives new formulas for these numbers, advancing understanding of their properties and relationships.
Contribution
It introduces new explicit evaluations of series with generalized harmonic numbers and derives formulas for these numbers, which were not previously known.
Findings
Explicit evaluations of certain infinite series involving generalized harmonic numbers.
New formulas for generalized (alternating) harmonic numbers.
Enhanced understanding of the properties of harmonic numbers.
Abstract
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Mathematical Inequalities and Applications