Explicit Evaluation of Euler and Related Sums
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.
KeywordsEuler 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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