Connection coefficients and zeros of orthogonal polynomials
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Data
2001-08-01
Autores
Dimitrov, D. K.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Elsevier B.V.
Resumo
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.
Descrição
Palavras-chave
connection coefficients, zeros of orthogonal polynomials, Descartes' rule of signs, Wronskians, inequalities for zeros
Como citar
Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 133, n. 1-2, p. 331-340, 2001.