Definition: Bernstein Polynomial
The polynomial
\[
B_i^n(u)=\binom{n}{i}\,u^i\,{(1-u)}^{n-i}\;,\quad i=0,\dotsc,n
\]
is called the \(i^{th}\) Bernstein polynomial of degree \(n\). Convention: \(B_i^n\equiv 0\), if \(i<0\) or \(i>n\).