Constructing Krall-Hahn orthogonal polynomials
Given a sequence of polynomials (pn)n, an algebra of operators A that acts in the linear space of polynomials and an operator Dp E A with Dp(pn) = =npn, where On is any arbitrary eigenvalue, we construct a new sequence of polynomials (qn)n by considering a linear combination of m+1 consecutive pn:qn...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182295 |
| Acceso en línea: | https://hdl.handle.net/11441/182295 https://doi.org/10.1016/j.jmaa.2014.10.069 |
| Access Level: | acceso abierto |
| Palabra clave: | Difference operators and equations Hahn polynomial Krall polynomial Orthogonal polynomial |
| Sumario: | Given a sequence of polynomials (pn)n, an algebra of operators A that acts in the linear space of polynomials and an operator Dp E A with Dp(pn) = =npn, where On 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 + ∑mj=1 Bnjpn-j. Using the concept of a D-operator, we determine the structure of the sequences Bnj,j = 1,…,m, such 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 that are also eigenfunctions of higher-order difference operators. |
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