Communications of the
Korean Mathematical Society CKMS

Formal manipulations of double series are useful in getting some other identities from given ones and evaluating certain summations, involving double series. The main object of this note is to summarize rather useful double series manipulations scattered in the literature and give their generalized formulas, for convenience and easier reference in their future use. An application of such manipulations to an evaluation for Euler sums (in itself, interesting), among other things, will also be presented to show usefulness of such manipulative techniques.

Keywords: double series manipulations, Riemann Zeta function, generalized harmonic numbers, harmonic numbers, Euler sums

MSC numbers: Primary 33-00, 40A25; Secondary 11L99