Bispectral Laguerre type polynomials

2019/05/22 by Durán, Antonio J., de la Iglesia, Manuel D.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.09223

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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