Characterization of the generalized Chebyshev-type polynomials of first kind

Abstract

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-type polynomials of the first kind ${\mathcal{T}}_n^{(M,N)}(x),$ 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 weighted generalized Chebyshev-type with the Bernstein polynomials.

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Cited by in corpus (1)

• Change of basis for generalized Chebyshev Koornwinder's type polynomials of first kind