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Generalized Bernstein Polynomials
BIT Numerical Mathematics, 2004The authors define generalized Bernstein polynomials of degree \(n\), for \(n \in \mathbb{N}\) and \(i \in \{0,1,\dots,n\}\), by \[ B_i^n(x;\omega| q):= \frac{1}{(\omega;q)_n} \begin{bmatrix} n \\i \end{bmatrix}_q x^i(\omega x^{-1};q)_i(x;q)_{n-i}. \] Here \(q\) and \(\omega\) are real parameters such that \(q \neq 1\) and \(\omega \neq 1,q^{-1},\dots ...
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