Orthogonal Polynomial Solutions of Differential Equations

2010 ◽  
pp. 79-93
Author(s):  
Roelof Koekoek ◽  
Peter A. Lesky ◽  
René F. Swarttouw
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomial ◽  
Polynomial Solutions

scholarly journals On a Symmetric Generalization of Bivariate Sturm–Liouville Problems

2021 ◽  
Author(s):  
Yves Guemo Tefo ◽  
Rabia Aktaş ◽  
Iván Area ◽  
Esra Güldoğan Lekesiz
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Orthogonal Polynomial ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Polynomial Solutions ◽  
New Class ◽  
Polynomial Coefficients ◽  
Sturm Liouville ◽  
Hypergeometric Type

AbstractA new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation is presented and orthogonality is obtained using the Sturm–Liouville approach. Conditions on the polynomial coefficients to have admissible partial differential equations are given. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for the monic orthogonal polynomial solutions, as well as explicit form of these monic orthogonal polynomial solutions, which are solutions of an admissible and potentially self-adjoint linear second-order partial differential equation of hypergeometric type.

The Krall Polynomials as Solutions to a Second Order Differential Equation

1983 ◽  
Vol 26 (4) ◽  
pp. 410-417 ◽  
Author(s):  
Lance L. Littlejohn
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Order Differential Equation ◽  
Order Equation ◽  
Second Order ◽  
Polynomial Solutions ◽  
Second Order Differential Equations ◽  
Image Position

AbstractA popular problem today in orthogonal polynomials is that of classifying all second order differential equations which have orthogonal polynomial solutions. We show that the Krall polynomials satisfy a second order equation of the form1.1

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