Some Harmonic Number Identities involving certain Reciprocals
Maarten Kronenburg
TL;DR
This paper evaluates finite series of harmonic numbers involving reciprocals, expands products of reciprocals into sums, and provides a computer program with examples to facilitate calculations.
Contribution
It introduces new identities for harmonic number series involving reciprocals and offers a computational tool for their evaluation.
Findings
Derived new harmonic number identities involving reciprocals
Developed a computer program to evaluate these series
Provided illustrative examples of the identities
Abstract
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Theories and Applications · Advanced Mathematical Identities