A characterization of the four Chebyshev orthogonal families

Abstract

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. Copyright © 2005 Hindawi Publishing Corporation.