Characterization of the Generalized Chebyshev Polynomials of First Kind

Mohammad A. AlQudah

Published 2015-03-25Version 1

Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials. In this paper, we characterize the generalized Chebyshev orthogonal polynomials of the first kind $\mathscr{T}_{n}^{(M,N)}(x),$ then we provide a closed form of the constructed polynomials in term of the Bernstein polynomials $B_{k}^{n}(x).$ We conclude the paper with some results on the integration of the product of the weighted generalized Chebyshev polynomials with the Bernstein polynomials.