Monotonicity of zeros of Jacobi polynomials
dc.contributor | Universidade Estadual Paulista (Unesp) | |
dc.date.accessioned | 2014-05-20T14:01:33Z | |
dc.date.available | 2014-05-20T14:01:33Z | |
dc.date.created | 2014-05-20T14:01:33Z | |
dc.date.issued | 2007-11-01 | |
dc.identifier | Journal of Approximation Theory. San Diego: Academic Press Inc. Elsevier B.V., v. 149, n. 1, p. 15-29, 2007. | |
dc.identifier | 0021-9045 | |
dc.identifier | http://hdl.handle.net/11449/21723 | |
dc.identifier | 10.1016/j.jat.2007.04.004 | |
dc.identifier | WOS:000251646600002 | |
dc.identifier | WOS000251646600002.pdf | |
dc.description.abstract | Denote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved. | |
dc.language | eng | |
dc.publisher | Elsevier B.V. | |
dc.relation | Journal of Approximation Theory | |
dc.relation | 0.939 | |
dc.relation | 0,907 | |
dc.rights | Acesso aberto | |
dc.source | Web of Science | |
dc.subject | zeros | |
dc.subject | Jacobi polynomials | |
dc.subject | monotonicity | |
dc.title | Monotonicity of zeros of Jacobi polynomials | |
dc.type | Artículos de revistas |