Generalized Bernstein Polynomials
- Cite this article as:
- Lewanowicz, S. & Woźny, P. BIT Numerical Mathematics (2004) 44: 63. doi:10.1023/B:BITN.0000025086.89121.d8
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We introduce polynomials Bni(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 Bni(x;ω|q), big q-Jacobi and q-Hahn (or dual q-Hahn) polynomials are presented.