Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II

TL;DR

This paper conjectures recurrence relations with constant coefficients for multi-indexed orthogonal polynomials, extending previous work on variable-dependent relations, and identifies the simplest relations with specific term counts.

Contribution

It introduces conjectured constant coefficient recurrence relations for multi-indexed orthogonal polynomials, expanding understanding of their algebraic structure.

Findings

Recurrence relations with constant coefficients are conjectured for these polynomials.

The simplest relations have 3+2ℓ terms, with ℓ ≥ M.

Extension of previous variable-dependent recurrence relations.

Abstract

In a previous paper we presented $3+2M$ term recurrence relations with variable dependent coefficients for $M$-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. In this paper we present (conjectures of) the recurrence relations with constant coefficients for these multi-indexed orthogonal polynomials. The simplest recurrence relations have $3+2\ell$ terms, where $\ell (\geq M)$ is the degree of the lowest member of the multi-indexed orthogonal polynomials.