BIT Numerical Mathematics

, Volume 44, Issue 1, pp 63–78

Generalized Bernstein Polynomials

  • Stanisław Lewanowicz
  • Paweł Woźny

DOI: 10.1023/B:BITN.0000025086.89121.d8

Cite this article as:
Lewanowicz, S. & Woźny, P. BIT Numerical Mathematics (2004) 44: 63. doi:10.1023/B:BITN.0000025086.89121.d8


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.

generalized Bernstein polynomialsgeneralized Bézier formgeneralized de Casteljau algorithmdegree elevationbig q-Jacobi polynomialsq-Hahn polynomialsdual q-Hahn polynomialsorthogonal polynomial expansion

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Stanisław Lewanowicz
    • 1
  • Paweł Woźny
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland