A $q$-generalization of the para-Racah polynomials
Classical Analysis and ODEs
2017-08-14 v1
Abstract
New bispectral orthogonal polynomials are obtained from an unconventional truncation of the Askey-Wilson polynomials. In the limit , 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 -generalization of the para-Krawtchouk polynomials is obtained as a special case. Connections with the -Racah and dual-Hahn polynomials are also presented.
Keywords
Cite
@article{arxiv.1708.03368,
title = {A $q$-generalization of the para-Racah polynomials},
author = {Jean-Michel Lemay and Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:1708.03368},
year = {2017}
}
Comments
13 pages