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<p>This paper classifies the contiguity relations for finite families of polynomials within the (<i>q</i>-)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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Nicolas Crampé,
  • Lucia Morey,
  • Luc Vinet,
  • Meri Zaimi

摘要

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.