New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers
Number Theory
2015-09-01 v1
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 perhaps the discovery of several previously unknown infinite summation results involving {\em non-linear} generalized harmonic number terms and the derivation of interesting alternating summation formulas involving these numbers
Cite
@article{arxiv.1508.07345,
title = {New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers},
author = {Kunle Adegoke and Olawanle Layeni},
journal= {arXiv preprint arXiv:1508.07345},
year = {2015}
}