arXiv:1112.4230 Abstract | arXiv Analytics

arXiv:1112.4230 [math.CA]Abstract References Reviews Resources

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

Published 2011-12-19, updated 2012-09-28Version 2

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.

Comments: 29 pages. Typos corrected. Subsection 4.3 is modified

Categories: math.CA, math.QA

Subjects: 33D52, 33D67

Keywords: multiple basic hypergeometric series, difference operators, van diejens, transformation formula, kernel identities

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