Multi-indexed Wilson and Askey-Wilson Polynomials

Abstract

As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of 'virtual state solutions' of type I and II, in a similar way to the multi-indexed Laguerre, Jacobi and (q-)Racah polynomials reported earlier.

30 pages. Three references added. To appear in J.Phys.A. arXiv admin note: text overlap with arXiv:1203.5868

References in corpus (3)

• Reductions of lattice mKdV to $q$-${\mathrm{P}}_{VI}$
• Discrete Painleve II equation over finite fields
• Conserved quantities and generalized solutions of the ultradiscrete KdV equation

Cited by in corpus (1)

• From Polygons to Ultradiscrete Painlevé Equations