On Some Summation Formulas
Taekyun Kim, Dae San Kim, Hyunseok Kwon, Jongkyum Kwon
TL;DR
This paper derives new finite and infinite summation formulas involving Harmonic numbers using definite integrals, contributing to the mathematical understanding of harmonic series and summation techniques.
Contribution
It introduces novel summation formulas involving Harmonic numbers derived through integral methods, expanding existing mathematical tools.
Findings
New finite summation formula involving Harmonic numbers
Infinite summation formula involving Harmonic numbers
Use of definite integrals to derive summation identities
Abstract
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
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Taxonomy
TopicsAdvanced Mathematical Theories · Advanced Mathematical Theories and Applications · Advanced Mathematical Identities