The saalschütz chain reactions and multiple q-series transformations

Abstract

By recursive use of the q-Saalschütz summation formula, we investigate further the Saalschütz chain reactions introduced by the author in (Chu, 2002). Some general series transformations which express basic terminating series in terms of finite multiple sums will be established. As applications, we derive by means of Jackson's 6φ5-series identity three transformations including one due to Andrews (1975). These transformations yield further a number of multiple Rogers-Ramanujan identities, whose research was initiated and developed mainly by Andrews and Bressoud from the middle of seventieth up to now. © 2005 Springer Science+Business Media, Inc.