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Exceptional Charlier and Hermite orthogonal polynomials

Opened Access Exceptional Charlier and Hermite orthogonal polynomials

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Autor: Durán Guardeño, Antonio José
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2014-06
Publicado en: Journal of Approximation Theory, 182, 29-58
Tipo de documento: Artículo
Resumen: Using Casorati determinants of Charlier polynomials View the MathML source, we construct for each finite set F of positive integers a sequence of polynomials View the MathML source, n∈σF, which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF⊊N. For suitable finite sets F (we call them admissible sets), we prove that the polynomials View the MathML source, n∈σF, are actually exceptional Charlier 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 Charlier polynomials into a Wronskian determinant of Hermite polynomials. For admissible sets, these Wronskian determinants turn out to be exceptional Hermite polynomials.
Tamaño: 332.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/31985

DOI: http://dx.doi.org/10.1016/j.jat.2014.03.004

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