Factorization of Basic Hypergeometric Series

Abstract

The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general ₂𝜓₂ series is examined in detail. Connections are found with the theory of basic hypergeometric series on root systems. Alternative proofs of several well-known summation and transformation formulae, including Gustafson's generalization of Ramanujan's ₁𝜓₁ summation, are obtained incidentally.