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Distribution of zeros of discrete and continuous polynomials from their recurrence relation

Opened Access Distribution of zeros of discrete and continuous polynomials from their recurrence relation

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Autor: Álvarez Nodarse, Renato
Sánchez Dehesa, Jesús
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2002-05-25
Publicado en: Applied Mathematics and Computation, 128 (2-3), 167-190.
Tipo de documento: Artículo
Resumen: The hypergeometric polynomials in a continous or a discrete variable, whose canonical forms are the so-called classical orthogonal polynomial systems, are ob jects which naturally appear in a broad range of physical and mathematical elds from quantum mechanics, the theory of vibrating strings and the theory of group representations to numerical analysis and the theory of Sturm-Liouville di erential and di erence equations. Often, they are encountered in the form of a three term recurrence relation (TTRR) which connects a polynomial of a given order with the polynomial of the contiguous orders. This relation can be directly found, in particular, by use of Lanczos-type methods, tight-binding models or the application of the conventional discretisation procedures to a given di erential operator. Here the distribution of zeros and its asymptotic limit, characterized by means of its moments around the origin, are found for the continuous classical (Hermite, Laguerre, Jacobi, Bessel) poly...
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Cita: Álvarez Nodarse, R. y Sánchez Dehesa, J. (2002). Distribution of zeros of discrete and continuous polynomials from their recurrence relation. Applied Mathematics and Computation, 128 (2-3), 167-190.
Tamaño: 299.2Kb
Formato: PDF

URI: http://hdl.handle.net/11441/41700

DOI: http://dx.doi.org/10.1016/S0096-3003(01)00071-6

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