Discrete Orthogonality Relations for the Multi-Indexed Orthogonal Polynomials in Discrete Quantum Mechanics with Pure Imaginary Shifts

Abstract

The discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts are investigated. We show that the discrete orthogonality relations hold for the case-(1) multi-indexed orthogonal polynomials of continuous Hahn, Wilson and Askey-Wilson types, and conjecture their normalization constants.

32 pages. A reference and comments are added. To shorten the length, Section 4 and Appendix B are deleted. To appear in J.Math.Phys

References in corpus (6)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Orthogonal Polynomials from Hermitian Matrices
• Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
• Dual Christoffel transformations
• Multi-indexed Meixner and Little $q$-Jacobi (Laguerre) Polynomials
• Perturbations around the zeros of classical orthogonal polynomials