Characterization of the generalized Chebyshev-type polynomials of first kind
نویسنده
چکیده
Orthogonal polynomials have very useful properties in the mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials. In this paper, we characterize a sequence of the generalized Chebyshev-type polynomials of the first kind { T (M,N) n (x) } n∈N∪{0} , which are orthogonal with respect to the measure √ 1−x2 π dx + Mδ−1 + Nδ1, where δx is a singular Dirac measure and M,N ≥ 0. Then we provide a closed form of the constructed polynomials in term of the Bernstein polynomials B k (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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