Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II

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 $\ell (\ge M)$ is the degree of the lowest member of the multi-indexed orthogonal polynomials.

arXiv comment27 pages. Comments, references and examples added, reference information updated. To appear in J.Math.Phys

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Cited by in corpus (7)

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• Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types
• New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and $q$-Racah types
• Dual Polynomials of the Multi-Indexed ($q$-)Racah Orthogonal Polynomials
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types