Bernstein polynomial/Definition

Definition

The $n$^th Bernstein polynomial for a function $f:I\rightarrow\mathbb{R}$ (where $I:\eq[0,1]\subset\mathbb{R}$ is the closed unit interval) is defined as follows:

• $$\mathcal{B}_n(f;x):\eq\sum^n_{i\eq 0}{}^nC_if\left(\tfrac{k}{n}\right)x^i(1-x)^{n-i}$$