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The Ramanujan Journal

, Volume 37, Issue 1, pp 89–108 | Cite as

A family of shifted harmonic sums

  • Anthony SofoEmail author
  • H. M. Srivastava
Article

Abstract

In this paper, we first develop a set of identities for Euler-type sums. We then investigate products of the shifted harmonic numbers and the reciprocal binomial coefficients. We briefly indicate relevant connections of the results presented here with those given by earlier authors. As by-products of our investigation, we derive several (presumably new) one-parameter and two-parameter summation formulas for the hypergeometric series \(\;_3F_2\;\) at argument 1.

Keywords

Harmonic numbers Riemann Zeta function Integral representations Binomial coefficients Euler sums Psi (or Digamma) function Polygamma functions 

Mathematics Subject Classification

Primary 05A10 05A19 Secondary 11B83 11M06 33B15 33C20 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Section of Mathematics, VU CollegeVictoria University of TechnologyMelbourneAustralia
  2. 2.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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