Multi-indexed (q)-Racah Polynomials

Details Multi-indexed (q)-Racah Polynomials Multi-indexed (q)-Racah Polynomials

2012-03-27

arxiv.org/abs/1203.5868v1

Physics

Mathematical Physics

39 pages

Scientific paper

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 of type I and II, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the `solutions' of the matrix Schr\"odinger equation with negative `eigenvalues', except for one of the two boundary points.

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