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 we conjecture their normalization constants.