# Bernstein polynomial

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## Definition

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

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