A Generalization of Andrews' Reduction Formula for the Rogers-Selberg Functions

Abstract

Andrews' reduction formula for the Rogers-Selberg functions leads to striking multiple series identities of great elegance which imply Gordon's infinite family of partition theorems of Rogers-Ramanujan type. All known proofs of Andrews' reduction formula depend either on q-difference equation arguments or the use of the transformation theory of basic hypergeometric series. In this paper we give a simple direct proof of a generalization of Andrews' reduction formula. Our formula deals with a yet more general function of Rogers which is directly related to several recent important discoveries in the theory of partitions.