Bernstein polynomial

Definition

Let $f \colon [0, 1] \to \mathbb{R}$ be a function and let $n \ge 1$ be an integer. The $n$-th Bernstein polynomial of $f$ is $$B_n(f)(x) = \sum_{k=0}^{n} f\Big( \frac{k}{n} \Big) \binom{n}{k} x^k (1 - x)^{n-k}.$$ The polynomials $b_{k,n}(x) = \binom{n}{k} x^k (1 - x)^{n-k}$ are the Bernstein basis polynomials.