Journal of Analysis & Number Theory
Journal license

Journal

Journal of Analysis & Number Theory


Volume
& Issue

Volume 4, Issue 1


Published
on

January 1, 2016


Pages

49-60


DOI

Article

New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers

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Authors

Kunle Adegoke* Affiliation:
Department of Physics and Engineering Physics, Obafemi Awolowo University, Ile-Ife, 220005 Nigeria
and Olawanle Layeni Affiliation:
Department of Mathematics, Obafemi Awolowo University, Ile-Ife, 220005 Nigeria


Abstract

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both finite and infinite sums. The high points of this paper are the discovery of several previously unknown infinite summation results involving non-linear generalized harmonic number terms and the derivation of interesting alternating summation formulas involving these numbers.


Keywords

harmonic numbers, Riemann zeta function, polygamma function, polylogarithm function, Bernoulli number, Euler number, summation identity


Citation

Adegoke, K. & Layeni, O. (2016). New finite and infinite summation identities involving the generalized harmonic numbers. Journal of Analysis & Number Theory, 4(1), 49–60. https://doi.org/10.18576/jant/040108

Published by: Engineering Journals

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