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Explicit Evaluation of Euler and Related Sums
 Junesang Choi,
 H. M. Srivastava
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Ever since the time of Euler, the socalled 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 R052003104410. 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
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 Title
 Explicit Evaluation of Euler and Related Sums
 Journal

The Ramanujan Journal
Volume 10, Issue 1 , pp 5170
 Cover Date
 20050801
 DOI
 10.1007/s1113900535056
 Print ISSN
 13824090
 Online ISSN
 15729303
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 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
 TaylorMaclaurin series
 Gauss summation theorem
 Industry Sectors
 Authors

 Junesang Choi ^{(1)}
 H. M. Srivastava ^{(2)}
 Author Affiliations

 1. Department of Mathematics, College of Natural Sciences, Dongguk University, Kyongju, 780714, Korea
 2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada, V8W 3P4