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arXiv · 2504.20802

Contiguity relations for finite families of orthogonal polynomials in the Askey scheme

Nicolas Crampé·Lucia Morey·Luc Vinet·Meri Zaimi
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Abstract

This paper classifies the contiguity relations for finite families of polynomials within the ($q$-)Askey scheme. The necessary and sufficient conditions for the existence of these contiguity relations are presented first. These conditions are then solved, yielding a comprehensive list of contiguity relations for these various families of polynomials. Furthermore, we demonstrate that all contiguity relations correspond to spectral transforms.

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Nicolas Crampé, Lucia Morey, Luc Vinet, Meri Zaimi. 2025-04-29. Contiguity relations for finite families of orthogonal polynomials in the Askey scheme. https://arxiv.org/abs/2504.20802

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