Some Generalized Harmonic Number Identities
Number Theory
2012-02-10 v2 Combinatorics
Abstract
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite series of generalized harmonic numbers involving nonnegative integer powers, which can be used to evaluate the sums of the finite series of generalized harmonic numbers involving polynomials. Many examples and a computer program are provided.
Cite
@article{arxiv.1103.5430,
title = {Some Generalized Harmonic Number Identities},
author = {Maarten Kronenburg},
journal= {arXiv preprint arXiv:1103.5430},
year = {2012}
}
Comments
Added examples, computer program and some textual corrections