Artículos de revistas
Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials
Applied Numerical Mathematics. Amsterdam: Elsevier B.V., v. 36, n. 2-3, p. 321-331, 2001.
Universidade Estadual Paulista (Unesp)
Fac Univ Notre Dame Paix
It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.
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Univ Vigo; Universidade Estadual Paulista (UNESP); Universidade Estadual de Campinas (UNICAMP) (Amer Mathematical Soc, 2013-04-01)In this paper we obtain sharp bounds for the zeros of classical orthogonal polynomials of a discrete variable, considered as functions of a parameter, by using a theorem of A. Markov and the so-called Hellmann-Feynman ...