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arXiv · 1708.03368

A $q$-generalization of the para-Racah polynomials

Jean-Michel Lemay·Luc Vinet·Alexei Zhedanov
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Abstract

New bispectral orthogonal polynomials are obtained from an unconventional truncation of the Askey-Wilson polynomials. In the limit $q \to 1$, they reduce to the para-Racah polynomials which are orthogonal with respect to a quadratic bi-lattice. The three term recurrence relation and q-difference equation are obtained through limits of those of the Askey-Wilson polynomials. An explicit expression in terms of hypergeometric series and the orthogonality relation are provided. A $q$-generalization of the para-Krawtchouk polynomials is obtained as a special case. Connections with the $q$-Racah and dual-Hahn polynomials are also presented.

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Jean-Michel Lemay, Luc Vinet, Alexei Zhedanov. 2017-08-10. A $q$-generalization of the para-Racah polynomials. https://arxiv.org/abs/1708.03368

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