TRIPLE SUMS AND THE RIEMANN ZETA-FUNCTION

As a natural counterpart of classical double sum identities due to Euler, N. Nielsen, Ramanujan, and others, various relations between triple sums of the form [GRAPHICS] are here established. Among others, they may be used to derive explicit representations of these series in terms of the Riemann zeta function and products of it. The matter is carried out in detail for the cases p greater-than-or-equal-to 2, q = r = 1 as well as p + q + r less-than-or-equal-to 6. (C) 1994 Academic Press, Inc.