, Volume 10, Issue 1, pp 51-70

Explicit Evaluation of Euler and Related Sums

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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.

Research of the first author was supported by Korea Science and Engineering Foundation Grant R05-2003-10441-0. Research of the second author was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0007353.
2000 Mathematics Subject Classification: Primary–11M06, 33B15, 33E20; Secondary–11M35, 11M41, 33C20