Euler sums evaluatable from integrals
Commun. Korean Math. Soc. 2004 Vol. 19, No. 3, 545-555
Printed September 1, 2004
Myungho Jung, Young Joon Cho, Junesang Choi
Pusan National University, Pusan National University, Dongguk University
Abstract : Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a proof of the classical Euler sum by following Lewin's method. We also consider some related formulas involving Euler sums, which are evaluatable from some known definite integrals.
Keywords : Euler sums, Gamma function, (generalized) harmonic numbers, Psi function, Polygamma function, Riemann Zeta function, Hurwitz Zeta function, Polylogarithm function
MSC numbers : Primary 42A24, 11M99; Secondary{\linebreak} 33B15, 42A16
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