Opened Access Constructing Krall-Hahn orthogonal polynomials

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Autor: Durán Guardeño, Antonio José
Domínguez de la Iglesia, Manuel
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2015-04-01
Publicado en: Journal of Mathematical Analysis and Applications, 424 (1), 361-384.
Tipo de documento: Artículo
Resumen: Given a sequence of polynomials (pn)n, an algebra of operators A acting in the linear space of polynomials and an operator Dp ∈ A with Dp(pn) = θnpn, where θn is any arbitrary eigenvalue, we construct a new sequence of polynomials (qn)n by considering a linear combination of m + 1 consecutive pn: qn = pn + Pm j=1 βn,jpn−j . Using the concept of D-operator, we determine the structure of the sequences βn,j , j = 1, . . . , m, in order that the polynomials (qn)n are eigenfunctions of an operator in the algebra A. As an application, from the classical discrete family of Hahn polynomials we construct orthogonal polynomials (qn)n which are also eigenfunctions of higherorder difference operators.
Cita: Durán Guardeño, A.J. y Domínguez de la Iglesia, M. (2015). Constructing Krall–Hahn orthogonal polynomials. Journal of Mathematical Analysis and Applications, 424 (1), 361-384.
Tamaño: 317.9Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42908

DOI: 10.1016/j.jmaa.2014.10.069

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