Evaluation of Euler-like sums via Hurwitz zeta values

Authors

AYHAN DİL
ISTVAN MEZO
MEHMET CENKCİ

DOI

10.3906/mat-1603-4

Abstract

In this paper we collect two generalizations of harmonic numbers (namelygeneralized harmonic numbers and hyperharmonic numbers) under one roof.Recursion relations, closed-form evaluations, and generating functions of thisunified extension are obtained. In light of this notion we evaluate someparticular values of Euler sums in terms of odd zeta values. We alsoconsider the noninteger property and some arithmetical aspects of this unifiedextension.

Keywords

Harmonic numbers, hyperharmonic numbers, generalized harmonic numbers, Euler sums, multiple zeta functions, Riemann zeta function, Hurwitz zeta function

First Page

1640

Last Page

1655

Recommended Citation

DİL, AYHAN; MEZO, ISTVAN; and CENKCİ, MEHMET (2017) "Evaluation of Euler-like sums via Hurwitz zeta values," Turkish Journal of Mathematics: Vol. 41: No. 6, Article 22. https://doi.org/10.3906/mat-1603-4
Available at: https://journals.tubitak.gov.tr/math/vol41/iss6/22