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arXiv · 1203.5868

Multi-indexed (q-)Racah Polynomials

Satoru Odake·Ryu Sasaki
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Abstract

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of `virtual state' vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the `solutions' of the matrix Schrödinger equation with negative `eigenvalues', except for one of the two boundary points.

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Satoru Odake, Ryu Sasaki. 2012-08-01. Multi-indexed (q-)Racah Polynomials. https://doi.org/10.1088/1751-8113%2F45%2F38%2F385201

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