scholarly journals Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or a q-quadratic lattice

2019 ◽  
Vol 25 (7) ◽  
pp. 969-993 ◽  
Author(s):  
Daniel Duviol Tcheutia
Keyword(s):  
Orthogonal Polynomial ◽  
Classical Orthogonal Polynomial ◽  
Polynomial Solutions ◽  
Recurrence Equations ◽  
Quadratic Lattice

scholarly journals A characterization of the four Chebyshev orthogonal families

2005 ◽  
Vol 2005 (13) ◽  
pp. 2071-2079 ◽  
Author(s):  
E. Berriochoa ◽  
A. Cachafeiro ◽  
J. M. Garcia-Amor
Keyword(s):  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Linear Combinations ◽  
Classical Orthogonal Polynomial ◽  
Polynomial Sequences ◽  
Fixed Length ◽  
Constant Coefficients ◽  
Fourth Kind

We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences.

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