Factorization of Basic Hypergeometric Series - Bradley-Thrush, Jonathan G. (Symmetry, integrability and geometry, methods and applications, 2025)
The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2ψ_2$ 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 $_1ψ_1$ summation, are obtained incidentally.