Atia, M. J. , Benabdallah, M. , COSTAS SANTOS, ROBERTO SANTIAGO
Si
Indag. Math.
Article
Científica
0.206
0.354
01/03/2012
000300811300004
2-s2.0-84856094359
In this paper we consider the monic polynomial sequence (P-n(alpha,q) (x)) that is orthogonal on [-1, 1] with respect to the weight function x(2q+1)(1 - x(2))(alpha)(1 - x), alpha > -1, q is an element of N; we obtain the coefficients of the tree-term recurrence relation (TTRR) by using a different method from the one derived in Atia et al. (2002) [2]; we prove that the interlacing property does not hold properly for (P-n(alpha,q) (x)); and we also prove that, if x(n,n)(alpha+i,q+j) is the largest zero of P-n(alpha+i,q+j) (x), x(2n-2j,2n-2j)(alpha+j,q+j) < x(2n-2i,2n-2i)(alpha+i,q+i) 0 <= i < j <= n - 1. Crown Copyright (C) 2011 Published by Elsevier B.V. on behalf of Royal Netherlands Academy of Arts and Sciences. All rights reserved.
Zeros; Real-rooted polynomials; Generalized Jacobi polynomials; Generalized Gegenbauer polynomials