Factorization of Basic Hypergeometric Series
Jonathan G. Bradley-Thrush
TL;DR
This paper explores the factorization of basic hypergeometric series, focusing on the $_2 ext{psi}_2$ case, and connects it with root system theory, providing new proofs of classical summation and transformation formulas.
Contribution
It introduces a comprehensive approach to factorizing basic hypergeometric series and links it to root system theory, offering alternative proofs of key identities.
Findings
Detailed analysis of $_2\psi_2$ series factorization
Connections established with root system hypergeometric series
New proofs of classical summation and transformation formulas
Abstract
The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general 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 summation, are obtained incidentally.
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