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arXiv · 1905.09223

Bispectral Laguerre type polynomials

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

We study the bispectrality of Laguerre type polynomials, which are defined by taking suitable linear combinations of a fixed number of consecutive Laguerre polynomials. These Laguerre type polynomials are eigenfunctions of higher-order differential operators and include, as particular cases, the Krall-Laguerre polynomials. As the main results, we prove that these Laguerre type polynomials always satisfy higher-order recurrence relations (i.e., they are bispectral). We also prove that the Krall-Laguerre families are the only 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. 2019-05-22. Bispectral Laguerre type polynomials. https://arxiv.org/abs/1905.09223

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