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Evaluation of Euler-like sums via Hurwitz zeta values. (English) Zbl 1424.11130
Summary: 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.

MSC:
11M32 Multiple Dirichlet series and zeta functions and multizeta values
40B05 Multiple sequences and series
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11M35 Hurwitz and Lerch zeta functions
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