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arXiv · 1112.4230

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

Yasuho Masuda
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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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Yasuho Masuda. 2012-09-28. Kernel identities for van Diejen's $q$-difference operators and transformation formulas for multiple basic hypergeometric series. https://arxiv.org/abs/1112.4230

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