On some infinite series of L. J. Mordell and their analogues

Abstract

In this paper we obtain a general reciprocity relation (Theorem 2.1) for a class of double series, from which we deduce several results including two alternating double series for f(3) (where (s) is the Riemann zeta function), which complement a result of L. J. Mordell. Later in the paper, we obtain another reciprocity relation for the double series and also extend our investigations to multiple series.