A q-generalization of the para-Racah polynomials

2017/08/10 by Lemay, Jean-Michel, Vinet, Luc, Zhedanov, Alexei · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.03368

Abstract

New bispectral orthogonal polynomials are obtained from an unconventional truncation of the Askey-Wilson polynomials. In the limit q → 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.

Cited by

• Perfect state transfer in inhomogeneous XX model of q-Racah type

Related

• The para-Racah polynomials
• Some Systems of Multivariable Orthogonal q-Racah polynomials
• A class of q-orthogonal polynomial sequences that extends the q-Askey scheme
• Linear partial divided-difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices
• Dual forms of the orthogonality relations of some classical q-orthogonal polynomials