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.
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Lewanowicz, S., Woźny, P. Generalized Bernstein Polynomials. BIT Numerical Mathematics 44, 63–78 (2004). https://doi.org/10.1023/B:BITN.0000025086.89121.d8
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DOI: https://doi.org/10.1023/B:BITN.0000025086.89121.d8