Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Beardon (1968)
On the convergence of Padé approximantsJournal of Mathematical Analysis and Applications, 21
C. Bernardi, Y. Maday (1991)
Progress in Approximation Theory
T. Koornwinder (1984)
Orthogonal Polynomials With Weight Function (1 - x) α ( l + x) β + M δ(x + 1) + Nδ(x - 1)Canadian Mathematical Bulletin, 27
R. Koekoek (1988)
Koornwinder's Laguerre polynomialsDelft Progress Report., 12
T. H. Koornwinder (1984)
Orthogonal polynomials with weight function (1αx) β(1+x) δ + Mδ(x+1+ Nδ(x —1)Canad. Math. Bull., 27
C. Bernardi, G. Coppoletta, Y. Maday (1992)
Some spectral approximations of two-dimensional fourth-order problemsMathematics of Computation, 59
(1991)
Polynômes orthogonaux de Laguerre–Hahn
J. Koekoek, R. Koekoek (1991)
On a differential equation for Koornwinder's generalized Laguerre polynomials, 112
K. Kwon, Sb Park (1997)
Two point masses perturbation of regular moment functionalsIndagationes Mathematicae, 8
A. Krall (1981)
Orthogonal polynomials satisfying fourth order differential equationsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 87
T. Chihara, A„y. Hendriksen (1985)
Orthogonal polynomials and mesures with end point massesRocky Mountain Journal of Mathematics, 15
G. Szegõ (1975)
Orthogonal Polynomials
H. L. Krall (1940)
On orthogonal polynomials satisfying a certain fourth order differential equationThe Pennsylvania State College Bull., 6
(1991)
Une théorie algébrique des polynômes orthogonaux: Applications aux polynômes
(1992)
comparative asymptotic for orthogonal polynomials, Math. USSR Sb
D. Griffel, T. Chihara (1979)
An Introduction to Orthogonal Polynomials
R. Álvarez-Nodarse, F. Marcellán (1996)
A generalization of the class laguerre polynomials: asymptotic properties and zerosApplicable Analysis, 62
H. Blatt, E. Saff, M. Simkani (1988)
Jentzsch-Szegö Type Theorems for the Zeros of Best ApproximantsJournal of The London Mathematical Society-second Series
Nadia Draïdi (1990)
Sur l'adjonction de deux masses de Dirac à une forme linéaire régulière quelconque
N. Draïdi, P. Maroni (1988)
Polinomios ortogonales y sus aplicaciones
A. Gončar (1975)
ON CONVERGENCE OF PADÉ APPROXIMANTS FOR SOME CLASSES OF MEROMORPHIC FUNCTIONSMathematics of The Ussr-sbornik, 26
G. Lopes (1989)
CONVERGENCE OF PADÉ APPROXIMANTS OF STIELTJES TYPE MEROMORPHIC FUNCTIONS AND COMPARATIVE ASYMPTOTICS FOR ORTHOGONAL POLYNOMIALSMathematics of The Ussr-sbornik, 64
J. Arves, F. Marcell, K. KwonPreprint (1998)
Some Extension of the Bessel-type Orthogonal Polynomials
E. Laguerre
Sur la réduction en fractions continues d'une fraction qui satisfait à une équation différentielle linéaire du premier ordre dont les coefficients sont rationnelsJournal de Mathématiques Pures et Appliquées, 1
(1999)
Analytic and Algebraic Properties of Polynomials with Several Models of Orthogonality: q-discretes, Sobolev-type and Semiclassicals
R. Álvarez-Nodarse, F. Marcell (1996)
A GENERALIZATION OF THE CLASSICAL LAGUERRE POLYNOMIALS . 1
Francisco Marcellán, P. Maroni (1992)
Sur l'adjonction d'une masse de Dirac á une forme régulière et semi-classiqueAnnali di Matematica Pura ed Applicata, 162
H. Bouakkaz, P. Maroni (1991)
Ann. Comput. Appl. Math.
P. Maroni (1991)
Une théorie algébrique des polynômes orthogonaux: Applications aux polynômes orthogonaux semiclassiquesAnn. Comput. Appl. Math., 9
R. Koekoek (1990)
Generalizations of the classical laguerre polynomials and some q-analogues
R. Álvarez-Nodarse, F. Marcelll
A Generalization of the Classical Laguerre Polynomials: Asymptotic Properties and Zeros. 1
A. Ronveaux, F. Marcellán (1989)
Differential Equation for Classical-Type Orthogonal PolynomialsCanadian Mathematical Bulletin, 32
R. Álvarez-Nodarse, F. Marcellán (1995)
A generalization of the classical Laguerre polynomialsRendiconti del Circolo Matematico di Palermo, 44
F. Olver (1974)
Asymptotics and Special Functions
(1988)
Koornwinder ’ s Laguerre polynomials , Delft Progress Report
J. Arvesú, R. Álvarez-Nodarse, F. Marcellán, K. Kwon (1998)
Some extension of the Bessel-type orthogonal polynomialsIntegral Transforms and Special Functions, 7
F. Marcellán, E. Prianes (1996)
Orthogonal polynomials and Stieltjes functions: The Laguerre-Hahn caseRend. Mat., 16
S. Belmehdi, F. Marcellán (1992)
Orthogonal polynomials associated with some modifications of a linear functionalApplicable Analysis, 46
W. Everitt, K. Kwon, L. Littlejohn, R. Wellman (2001)
Orthogonal polynomial solutions of linear ordinary dierential equations
The paper deals with orthogonal polynomials in the case where the orthogonality condition is related to semiclassical functionals. The polynomials that we discuss are a generalization of Jacobi polynomials and Jacobi-type polynomials. More precisely, we study some algebraic properties as well as the asymptotic behaviour of polynomials orthogonal with respect to the linear functional U U=J α,β+A 1δ(x−1)+B 1δ(x+1)−A 2δ′(x−1)−B 2δ′(x+1), where J α,β is the Jacobi linear functional, i.e. 《J α,β,p›=∫−1 1 p(x)(1−x)α(1+x)β dx,αα,β>−1, p∈P, and P is the linear space of polynomials with complex coefficients. The asymptotic properties are analyzed in (−1,1) (inner asymptotics) and C∖[−1,1] (outer asymptotics) with respect to the behaviour of Jacobi polynomials. In a second step, we use the above results in order to obtain the location of zeros of such orthogonal polynomials. Notice that the linear functional U is a generalization of one studied by T. H. Koornwinder when A 2=B 2=0. From the point of view of rational approximation, the corresponding Markov function is a perturbation of the Jacobi–Markov function by a rational function with two double poles at ±1. The denominators of the [n−1/n] Padé approximants are our orthogonal polynomials.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 10, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.