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

TL;DR

This paper investigates the discrete orthogonality relations of multi-indexed orthogonal polynomials within discrete quantum mechanics, establishing their validity for certain polynomial types and proposing conjectures for their normalization constants.

Contribution

It demonstrates the orthogonality relations for specific multi-indexed polynomials and conjectures their normalization constants, advancing understanding in discrete quantum mechanics.

Findings

Orthogonality relations hold for continuous Hahn, Wilson, and Askey-Wilson types.

Normalization constants are conjectured for these polynomials.

Provides a foundation for further exploration of multi-indexed orthogonal polynomials.

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.