English

Transformation formulas for bilinear sums of basic hypergeometric series

Classical Analysis and ODEs 2019-08-15 v3 Mathematical Physics math.MP Quantum Algebra Representation Theory

Abstract

A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic hypergeometric series of type AA with different dimensions and it can be considered as a generalization of Whipple-Sears transformation formula for terminating balanced 4ϕ3{}_4 \phi_3 series. As an application of the master formula, one variable cases of some transformation formulas for bilinear sums of basic hypergeometric series are given as examples. The bilinear transformation formulas seem to be new in the literature even in one variable case.

Keywords

Cite

@article{arxiv.1310.7676,
  title  = {Transformation formulas for bilinear sums of basic hypergeometric series},
  author = {Yasushi Kajihara},
  journal= {arXiv preprint arXiv:1310.7676},
  year   = {2019}
}

Comments

7 pages

R2 v1 2026-06-22T01:56:09.994Z