English

Kernel identities for van Diejen's $q$-difference operators and transformation formulas for multiple basic hypergeometric series

Classical Analysis and ODEs 2012-10-01 v2 Quantum Algebra

Abstract

In this paper, we show that the kernel function of Cauchy type for type BCBC intertwines the commuting family of van Diejen's qq-difference operators. This result gives rise to a transformation formula for certain multiple basic hypergeometric series of type BCBC. We also construct a new infinite family of commuting qq-difference operators for which the Koornwinder polynomials are joint eigenfunctions.

Keywords

Cite

@article{arxiv.1112.4230,
  title  = {Kernel identities for van Diejen's $q$-difference operators and transformation formulas for multiple basic hypergeometric series},
  author = {Yasuho Masuda},
  journal= {arXiv preprint arXiv:1112.4230},
  year   = {2012}
}

Comments

29 pages. Typos corrected. Subsection 4.3 is modified

R2 v1 2026-06-21T19:53:30.910Z