International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 13, Pages 2071-2079

A characterization of the four Chebyshev orthogonal families

E. Berriochoa,1 A. Cachafeiro,2 and J. M. Garcia-Amor3

1Departamento de Matemática Aplicada I, Facultad de Ciencias de Ourense, Universidad de Vigo, Ourense 32004, Spain
2Departamento de Matemática Aplicada I, ETS Ingenieros Industriales, Universidad de Vigo, Vigo 36280, Spain
3Departamento de Matemática, IES Gonzalo Torrente Ballester, Pontevedra 36003, Spain

Received 26 September 2004; Revised 2 June 2005

Copyright © 2005 E. Berriochoa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.