Characterization of the generalized Chebyshev-type polynomials of first kind

الأصل · EN

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 Tₙ⁽ᵐ,ⁿ⁾(x), then we provide a closed form of the constructed polynomials in term of the Bernstein polynomials Bₖⁿ(x). We conclude the paper with some results on the integration of the weighted generalized Chebyshev-type with the Bernstein polynomials.