# Bernstein B

The Bernstein basis polynomials $b_k^n$ are defined by $$b_k^n(x)={n \choose k} x^k (1-x)^{n-k},$$ where ${n \choose k}$ denotes a Binomial coefficient. A Bernstein polynomial $B_n^k$ is defined as a linear combination of Bernstein basis polynomials, i.e. $$B_n^k(x) = \displaystyle\sum_{i=0}^n \beta_i b_{i,n},$$ where $\beta_i \in \mathbb{R}$.