Dual Polynomials of the Multi-Indexed ($q$-)Racah Orthogonal Polynomials
Satoru Odake

TL;DR
This paper studies dual polynomials of multi-indexed ($q$-)Racah orthogonal polynomials, revealing their properties as ordinary orthogonal polynomials and their application in exactly solvable discrete quantum mechanics.
Contribution
It introduces dual multi-indexed ($q$-)Racah polynomials, showing they satisfy three-term recurrence relations and higher-order difference equations, and constructs new quantum systems based on them.
Findings
Dual polynomials satisfy three-term recurrence relations.
Dual polynomials are ordinary orthogonal and Krall-type.
New exactly solvable quantum models are constructed.
Abstract
We consider dual polynomials of the multi-indexed (-)Racah orthogonal polynomials. The -indexed (-)Racah polynomials satisfy the second order difference equations and various () term recurrence relations with constant coefficients. Therefore their dual polynomials satisfy the three term recurrence relations and various -th order difference equations. This means that the dual multi-indexed (-)Racah polynomials are ordinary orthogonal polynomials and the Krall-type. We obtain new exactly solvable discrete quantum mechanics with real shifts, whose eigenvectors are described by the dual multi-indexed (-)Racah polynomials. These quantum systems satisfy the closure relations, from which the creation/annihilation operators are obtained, but they are not shape invariant.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
