Generalized Chebyshev polynomials of the second kind

Abstract

We characterize the generalized Chebyshev polynomials of the second kind\n(Chebyshev-II), and then we provide a closed form of the generalized\nChebyshev-II polynomials using the Bernstein basis. These polynomials can be\nused to describe the approximation of continuous functions by Chebyshev\ninterpolation and Chebyshev series and how to efficiently compute such\napproximations. We conclude the paper with some results concerning integrals of\nthe generalized Chebyshev-II and Bernstein polynomials.\n