English

Factorization of Basic Hypergeometric Series

Combinatorics 2025-07-08 v1 Classical Analysis and ODEs Quantum Algebra

Abstract

The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general 2ψ2_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 1ψ1_1\psi_1 summation, are obtained incidentally.

Keywords

Cite

@article{arxiv.2507.04313,
  title  = {Factorization of Basic Hypergeometric Series},
  author = {Jonathan G. Bradley-Thrush},
  journal= {arXiv preprint arXiv:2507.04313},
  year   = {2025}
}