Factorization of Basic Hypergeometric Series

The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general ${}_2{\psi }_2$ 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 ${}_1{\psi }_1$ summation, are obtained incidentally.