Orthogonal Polynomial Solutions of Real Difference Equations

2010 ◽  
pp. 95-121
Author(s):  
Roelof Koekoek ◽  
Peter A. Lesky ◽  
René F. Swarttouw
Keyword(s):  
Orthogonal Polynomial ◽  
Difference Equations ◽  
Real Difference ◽  
Polynomial Solutions

scholarly journals Two finite q-Sturm-Liouville problems and their orthogonal polynomial solutions

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 231-244 ◽  
Author(s):  
M. Masjed-Jamei ◽  
F. Soleyman ◽  
I. Area ◽  
J.J. Nieto
Keyword(s):  
Orthogonal Polynomial ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Continuous Case ◽  
Weight Functions ◽  
Polynomial Solutions ◽  
General Properties ◽  
Orthogonality Relations ◽  
Sturm Liouville

In this paper, we consider two new q-Sturm-Liouville problems and prove that their polynomial solutions are finitely orthogonal with respect to two weight functions which correspond to Fisher and Tstudent distributions as q ? 1. Then, we obtain the general properties of these polynomial solutions, such as orthogonality relations, three term recurrence relations, q-difference equations and basic hypergeometric representations, where all results in the continuous case are recovered as q ? 1.

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