Publication:
Jacobi-Sobolev-type orthogonal polynomials: Second-order differential equation and zeros

Thumbnail Image
Identifiers
URI: http://hdl.handle.net/10016/6405
ISSN: 0377-0427
DOI: 10.1016/S0377-0427(98)00005-3
Files
jacobi_arvesu_jcam_1998_ps.pdf (293.69 KB)
Publication date
1998-04-17
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
We obtain an explicit expression for the Sobolev-type orthogonal polynomials $\{Q_n\}$ associated with the inner product $\langle p,q\rangle=\int^1_{-1}p(x)q(x)\rho(x)dx+A_1p(1)q(1)+B_1p(-1)q(-1)+A_2p'(1)q'(1)+B_2p'(-1)q'(-1)$, where $\rho(x)=(1-x)^\alpha(1+x)^\beta$ is the Jacobi weight function, $\alpha,\beta>-1$, $A_1,B_1,A_2,B_2\geq 0$ and $p,q\in\bold P$, the linear space of polynomials with real coefficients. The hypergeometric representation $({}_6F_5)$ and the second-order linear differential equation that such polynomials satisfy are also obtained. The asymptotic behaviour of such polynomials in $[-1,1]$ is studied. Furthermore, we obtain some estimates for the largest zero of $Q_n(x)$. Such a zero is located outside the interval $[-1,1]$. We deduce its dependence on the masses. Finally, the WKB analysis for the distribution of zeros is presented.
Description
22 pages, 4 figures.-- MSC1991 codes: 33C45; 33A65; 42C05.-- Dedicated to Professor Mario Rosario Occorsio on his 65th birthday.
MR#: MR1624329 (99h:33029)
Zbl#: Zbl 0924.33006
Keywords
Orthogonal polynomials, Jacobi polynomials, Hypergeometric function, Sobolev-type orthogonal polynomials, WKB method
Bibliographic citation
Journal of Computational and Applied Mathematics, 1998, vol. 90, n. 2, p. 135-156
Collections
DM - GAMA - Artículos de Revistas