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arXiv · 1509.08213

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III

Satoru Odake
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Abstract

In a previous paper, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. In this paper we present a proof for the Laguerre and Jacobi cases. Their bispectral properties are also discussed, which give a method to obtain the coefficients of the recurrence relations explicitly. This paper extends to the Laguerre and Jacobi cases the bispectral techniques recently introduced by Gómez-Ullate et al. to derive explicit expressions for the coefficients of the recurrence relations satisfied by exceptional polynomials of Hermite type.

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Satoru Odake. 2016-01-20. Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III. https://doi.org/10.1063/1.4941087

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