, Volume 44, Issue 1, pp 63-78

Generalized Bernstein Polynomials

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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.