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arXiv · 1309.2346

Equivalences of the Multi-Indexed Orthogonal Polynomials

Satoru Odake
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Abstract

Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

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Satoru Odake. 2013-09-09. Equivalences of the Multi-Indexed Orthogonal Polynomials. https://doi.org/10.1063/1.4859795

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