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