Generalized Bernstein Polynomials |
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| Authors: | Stanisław Lewanowicz Paweł Woźny |
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| Affiliation: | (1) Institute of Computer Science, University of Wrocław, ul. Przesmyckiego 20, 51-151 Wrocław, Poland |
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| Abstract: | We introduce polynomials B n i (x;ω|q), depending on two parameters q and ω, which generalize classical Bernstein polynomials, discrete Bernstein polynomials defined by Sablonnière, as well as q-Bernstein polynomials introduced by Phillips. Basic properties of the new polynomials are given. Also, formulas relating B n i (x;ω|q), big q-Jacobi and q-Hahn (or dual q-Hahn) polynomials are presented. This revised version was published online in July 2006 with corrections to the Cover Date. |
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| Keywords: | generalized Bernstein polynomials generalized Bézier form generalized de Casteljau algorithm degree elevation big q-Jacobi polynomials q-Hahn polynomials dual q-Hahn polynomials orthogonal polynomial expansion |
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