Evaluation of Euler-like sums via Hurwitz zeta values | Zendy

Ayhan DİL | Zendy; István MEZÖ | Zendy; Mehmet CENKCİ | Zendy

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Evaluation of Euler-like sums via Hurwitz zeta values

Author(s) -

Ayhan DİL,

István MEZÖ,

Mehmet CENKCİ

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1603-4

Subject(s) - mathematics , arithmetic function , harmonic number , recursion (computer science) , euler's formula , pure mathematics , proof of the euler product formula for the riemann zeta function , property (philosophy) , extension (predicate logic) , riemann zeta function , harmonic , algebra over a field , discrete mathematics , arithmetic zeta function , mathematical analysis , prime zeta function , algorithm , philosophy , physics , epistemology , quantum mechanics , computer science , programming language

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

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