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.
Unable to display preview. Download preview PDF.