The Ramanujan Journal

, Volume 10, Issue 1, pp 51–70

Explicit Evaluation of Euler and Related Sums


DOI: 10.1007/s11139-005-3505-6

Cite this article as:
Choi, J. & Srivastava, H.M. Ramanujan J (2005) 10: 51. doi:10.1007/s11139-005-3505-6


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.


Euler sumsgamma function(generalized) harmonic numbersPsi functionpolygamma functionsrecurrence relations and recursion formulasRiemann Zeta functionHurwitz Zeta functionpolylogarithm functionshypergeometric seriesStirling numbers of the first kindTaylor-Maclaurin seriesGauss summation theorem

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