Complex Weight Functions for Classical Orthogonal Polynomials

1991 ◽  
Vol 43 (6) ◽  
pp. 1294-1308 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
David R. Masson ◽  
Mizan Rahman
Keyword(s):  
Orthogonal Polynomials ◽  
Weight Functions ◽  
Classical Orthogonal Polynomials ◽  
The Real ◽  
Complex Functions ◽  
Wilson Polynomials ◽  
Distributional Weight

AbstractWe give complex weight functions with respect to which the Jacobi, Laguerre, little q-Jacobi and Askey-Wilson polynomials are orthogonal. The complex functions obtained are weight functions in a wider range of parameters than the real weight functions. They also provide an alternative to the recent distributional weight functions of Morton and Krall, and the more recent hyperfunction weight functions of Kim.

Distributional Weight Functions and Orthogonal Polynomials

1979 ◽  
Author(s):  
Allan M. Krall
Keyword(s):  
Orthogonal Polynomials ◽  
Weight Functions ◽  
Distributional Weight

On the Askey-Wilson and Rogers Polynomials

1988 ◽  
Vol 40 (5) ◽  
pp. 1025-1045 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
Dennis Stanton
Keyword(s):  
Orthogonal Polynomials ◽  
Classical Orthogonal Polynomials ◽  
Wilson Polynomials ◽  
Image Position ◽  
Empty Product

The q-shifted factorial (a)n or (a; q)n isand an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials1.1where1.2and1.3We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [2].

Distributional Weight Functions for Orthogonal Polynomials

1978 ◽  
Vol 9 (4) ◽  
pp. 604-626 ◽  
Author(s):  
Robert D. Morton ◽  
Allan M. Krall
Keyword(s):  
Orthogonal Polynomials ◽  
Weight Functions ◽  
Distributional Weight

Orthogonal polynomials satisfying fourth order differential equations

1981 ◽  
Vol 87 (3-4) ◽  
pp. 271-288 ◽  
Author(s):  
Allan M. Krall
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Jacobi Polynomials ◽  
Weight Functions ◽  
Classical Orthogonal Polynomials ◽  
Absolutely Continuous ◽  
Independent Variable ◽  
Fourth Order Differential Equation

SynopsisThese polynomials, which are intimately connected with the Legendre, Laguerre and Jacobi polynomials, are orthogonal with respect to Stieltjes weight functions which are absolutely continuous on (− 1, 1), (0, ∞) and (0, 1), respectively, but which have jumps at some of the intervals' ends. Each set satisfies a fourth order differential equation of the form Ly = λny, where the coefficients of the operator L depends only upon the independent variable. The polynomials also have other properties, which are usually associated with the classical orthogonal polynomials.

scholarly journals Menke points on the real line and their connection to classical orthogonal polynomials

2010 ◽  
Vol 233 (6) ◽  
pp. 1416-1431
Author(s):  
P. Mathur ◽  
J.S. Brauchart ◽  
E.B. Saff
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Classical Orthogonal Polynomials ◽  
The Real

scholarly journals On Koornwinder classical orthogonal polynomials in two variables

2012 ◽  
Vol 236 (15) ◽  
pp. 3817-3826 ◽  
Author(s):  
Lidia Fernández ◽  
Teresa E. Pérez ◽  
Miguel A. Piñar
Keyword(s):  
Orthogonal Polynomials ◽  
Classical Orthogonal Polynomials
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