Kernel identities for van Diejen’s q-difference operators and transformation formulas for multiple basic hypergeometric series |
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Authors: | Yasuho Masuda |
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Institution: | 1. Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501, Japan
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Abstract: | The kernel function of Cauchy type for type BC is defined as a solution of linear q-difference equations. In this paper, we show that this kernel function 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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