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arXiv · 2012.07618

Bispectral Jacobi type polynomials

Antonio J. Durán·Manuel D. de la Iglesia
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Abstract

We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi type polynomials include, as particular cases, the Krall-Jacobi polynomials. As the main results we prove that the Jacobi type polynomials always satisfy higher-order recurrence relations (i.e., they are bispectral). We also prove that the Krall-Jacobi families are the only Jacobi type polynomials which are orthogonal with respect to a measure on the real line.

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Antonio J. Durán, Manuel D. de la Iglesia. 2020-12-14. Bispectral Jacobi type polynomials. https://arxiv.org/abs/2012.07618

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