Connection coefficients and zeros of orthogonal polynomials
We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2001 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/21710 |
| Acceso en línea: | http://dx.doi.org/10.1016/S0377-0427(00)00653-1 http://hdl.handle.net/11449/21710 |
| Access Level: | acceso abierto |
| Palabra clave: | connection coefficients zeros of orthogonal polynomials Descartes' rule of signs Wronskians inequalities for zeros |
| Sumario: | We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved. |
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