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

M. V. Subba Rao and R. Sitaramachandra Rao

Vol. 119 (1985), No. 1, 245–255

DOI: 10.2140/pjm.1985.119.245

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 ζ(3) (where ζ(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.

Mathematical Subject Classification 2000

Primary: 11N99

Secondary: 11B73

Milestones

Received: 14 July 1982

Revised: 2 May 1984

Published: 1 September 1985