Communications of the
Korean Mathematical Society CKMS

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