Abstract
ABSTRACTWe 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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