Orthogonal Polynomials Defined by Difference Equations

1941 ◽  
Vol 63 (1) ◽  
pp. 185 ◽  
Author(s):  
Otis E. Lancaster
Keyword(s):  
Orthogonal Polynomials ◽  
Difference Equations

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.

scholarly journals Difference equations for some orthogonal polynomials

1969 ◽  
Vol 28 (2) ◽  
pp. 383-392
Author(s):  
H. L. Krall ◽  
I. M. Sheffer
Keyword(s):  
Orthogonal Polynomials ◽  
Difference Equations

Asymptotic expansion of orthogonal polynomials via difference equations

2019 ◽  
Vol 239 ◽  
pp. 29-50 ◽  
Author(s):  
Xiao-Min Huang ◽  
Lihua Cao ◽  
Xiang-Sheng Wang
Keyword(s):  
Asymptotic Expansion ◽  
Orthogonal Polynomials ◽  
Difference Equations
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