On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials

Tom H. Koornwinder

On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials

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arxiv 1011.5585 v4 pith:IEYDEUR7 submitted 2010-11-25 math.CA

Tom H. Koornwinder This is my paper · ORCID

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keywords polynomialslimitq-jacobiq-racahformulagivenaskey-wilsonconceptual

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A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey-Wilson to Wilson polynomials and from q-Racah to Racah polynomials are given in a more conceptual way.

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The $q$-Racah polynomials from scalar products of Bethe states II
math-ph 2025-01 conditional novelty 6.0 of 10

The paper derives normalized scalar products of on-shell and off-shell Bethe states using Leonard triples, obtains explicit solutions of Belliard-Slavnov systems, and gives a determinant formula for q-Racah polynomials.

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