Evaluation of Euler-like sums via Hurwitz zeta values

Authors : Ayhan DİL, İstvan MEZO, Mehmet CENKCİ

Pages : 1640-1655

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper we collect two generalizations of harmonic numbers insert ignore into journalissuearticles values(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