Authors: AYHAN DİL, ISTVAN MEZO, MEHMET CENKCİ
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
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