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 intertwines the commuting family of van Diejen's -difference operators. This result gives rise to a transformation formula for certain multiple basic hypergeometric series of type . We also construct a new infinite family of commuting -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