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

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

2011-12-19

arxiv.org/abs/1112.4230v1

Mathematics

Classical Analysis and ODEs

28pages

Scientific paper

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

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