The Ramanujan Journal

, Volume 10, Issue 1, pp 51–70

Explicit Evaluation of Euler and Related Sums

Article

Abstract

Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a (presumably) new proof of the classical Euler sum. We show that several interesting analogues of the Euler sums can be evaluated by systematically analyzing some known summation formulas involving hypergeometric series. Many other identities related to the Euler sums are also presented.

Keywords

Euler sums gamma function (generalized) harmonic numbers Psi function polygamma functions recurrence relations and recursion formulas Riemann Zeta function Hurwitz Zeta function polylogarithm functions hypergeometric series Stirling numbers of the first kind Taylor-Maclaurin series Gauss summation theorem 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsCollege of Natural Sciences, Dongguk UniversityKyongjuKorea
  2. 2.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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