Generalized Tschebyscheff of the Second Kind and Bernstein Polynomials Change of Bases

Mohammad A AlQudah

Abstract

We construct multiple representations relative to different bases of the generalized Tschebyscheff polynomials of second kind. Also, we provide an explicit closed from of The generalized Polynomials of degree r less than or equal n in terms of the Bernstein basis of fixed degree n. In addition, we create the change-of-basis matrices between the generalized Tschebyscheff of the second kind polynomial basis and Bernstein polynomial basis. 

Keywords

Generalized Tschebyscheff, Bernstein Basis, Basis Transformation, B\'{e}zier Coefficient, Gamma function

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