A characterization of the four Chebyshev orthogonal families

We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant c...

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Main Authors:	E. Berriochoa, A. Cachafeiro, J. M. Garcia-Amor
Format:	Article
Language:	English
Published:	Hindawi Limited 2005-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/IJMMS.2005.2071

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spelling	doaj-cd68fd586d3f4fdd8301e4709e95d3b62020-11-24T20:48:55ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005132071207910.1155/IJMMS.2005.2071A characterization of the four Chebyshev orthogonal familiesE. Berriochoa0A. Cachafeiro1J. M. Garcia-Amor2Departamento de Matemática Aplicada I, Facultad de Ciencias de Ourense, Universidad de Vigo, Ourense 32004, SpainDepartamento de Matemática Aplicada I, ETS Ingenieros Industriales, Universidad de Vigo, Vigo 36280, SpainDepartamento de Matemática, IES Gonzalo Torrente Ballester, Pontevedra 36003, SpainWe obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences.http://dx.doi.org/10.1155/IJMMS.2005.2071
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	E. Berriochoa A. Cachafeiro J. M. Garcia-Amor
spellingShingle	E. Berriochoa A. Cachafeiro J. M. Garcia-Amor A characterization of the four Chebyshev orthogonal families International Journal of Mathematics and Mathematical Sciences
author_facet	E. Berriochoa A. Cachafeiro J. M. Garcia-Amor
author_sort	E. Berriochoa
title	A characterization of the four Chebyshev orthogonal families
title_short	A characterization of the four Chebyshev orthogonal families
title_full	A characterization of the four Chebyshev orthogonal families
title_fullStr	A characterization of the four Chebyshev orthogonal families
title_full_unstemmed	A characterization of the four Chebyshev orthogonal families
title_sort	characterization of the four chebyshev orthogonal families
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2005-01-01
description	We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences.
url	http://dx.doi.org/10.1155/IJMMS.2005.2071
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A characterization of the four Chebyshev orthogonal families

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