NOTES ON FORMAL MANIPULATIONS OF DOUBLE SERIES

Abstract. 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 Eu-ler sums (in itself, interesting), among other things, will also be presented to show usefulness of such manipulative techniques. 1. Introduction an