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arXiv · 1303.5820

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials

Satoru Odake
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Abstract

Ordinary orthogonal polynomials are uniquely characterized by the three term recurrence relations up to an overall multiplicative constant. We show that the newly discovered M-indexed orthogonal polynomials satisfy 3+2M term recurrence relations with non-trivial initial data of the lowest M+1 members. These include the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. The M=0 case is the corresponding classical orthogonal polynomials.

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Satoru Odake. 2013-03-23. Recurrence Relations of the Multi-Indexed Orthogonal Polynomials. https://doi.org/10.1063/1.4819255

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