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Exceptional Meixner and Laguerre orthogonal polynomials

Opened Access Exceptional Meixner and Laguerre orthogonal polynomials

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Autor: Durán Guardeño, Antonio José
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2014-08
Publicado en: Journal of Approximation Theory, 184, 176-208
Tipo de documento: Artículo
Resumen: Using Casorati determinants of Meixner polynomials (m a,c n )n, we construct for each pair F = (F1, F2) of finite sets of positive integers a sequence of polynomials m a,c;F n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials m a,c;F n , n ∈ σF , are actually exceptional Meixner polynomials; that is, in addition, they are orthogonal and complete with respect to a positive measure. By passing to the limit, we transform the Casorati determinant of Meixner polynomials into a Wronskian type determinant of Laguerre polynomials (L α n )n. Under the admissibility conditions for F and α, these Wronskian type determinants turn out to be exceptional Laguerre polynomials.
Tamaño: 363.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/31987

DOI: http://dx.doi.org/10.1016/j.jat.2014.05.009

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