scholarly journals Divided difference operators and classical orthogonal polynomials

1989 ◽  
Vol 19 (1) ◽  
pp. 33-38 ◽  
Author(s):  
Richard Askey
Keyword(s):  
Orthogonal Polynomials ◽  
Divided Difference ◽  
Difference Operators ◽  
Classical Orthogonal Polynomials

scholarly journals LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL EQUATIONS

1995 ◽  
Vol 10 (24) ◽  
pp. 1795-1802 ◽  
Author(s):  
YURI SMIRNOV ◽  
ALEXANDER TURBINER
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Difference Equations ◽  
Heisenberg Algebra ◽  
Difference Operators ◽  
Discrete Version ◽  
Classical Orthogonal Polynomials ◽  
Finite Difference Equations ◽  
Exactly Solvable

A certain representation for the Heisenberg algebra in finite difference operators is established. The Lie algebraic procedure of discretization of differential equations with isospectral property is proposed. Using sl 2-algebra based approach, (quasi)-exactly-solvable finite difference equations are described. It is shown that the operators having the Hahn, Charlier and Meissner polynomials as the eigenfunctions are reproduced in the present approach as some particular cases. A discrete version of the classical orthogonal polynomials (like Hermite, Laguerre, Legendre and Jacobi ones) is introduced.

Discrete inequalities, orthogonal polynomials and the spectral theory of difference operators

1992 ◽  
Vol 437 (1900) ◽  
pp. 355-373 ◽  
Keyword(s):  
Orthogonal Polynomials ◽  
Recurrence Relation ◽  
Moment Problem ◽  
Discrete Analogue ◽  
Difference Operators ◽  
Differential Inequalities ◽  
Classical Orthogonal Polynomials ◽  
Best Constant ◽  
Discrete Inequalities ◽  
Three Term Recurrence Relation

In a recent paper the first two authors studied a class of series inequalities associated with a three-term recurrence relation which includes a well-known inequality of Copson’s. It was shown that the validity of the inequality and the value of the best constant are determined in term s of the so-called Hellinger-Nevanlinnam -function. The theory is the discrete analogue of that established by Everitt for a class of integro-differential inequalities. In this paper the properties of the m -function are investigated and connections with the theory of orthogonal polynomials and the H am burger moment problem are explored. The results are applied to give examples of the series inequalities associated with the classical orthogonal polynomials.

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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