Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III

20 Jan 2016  ·  Odake Satoru ·

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 G\'omez-Ullate et al. to derive explicit expressions for the coefficients of the recurrence relations satisfied by exceptional polynomials of Hermite type. read more

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Mathematical Physics High Energy Physics - Theory Classical Analysis and ODEs Mathematical Physics Exactly Solvable and Integrable Systems