Bernstein polynomial basis (SciPy :WMA:
A Bernstein is a polynomial that is a linear combination of Bernstein basis polynomials.
With the advent of computer graphics, Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves.
BernsteinBasis[d,n,x] equals Binomial[d, n] x^n (1-x)^(d-n) in the interval [0, 1] and zero elsewhere.
BernsteinBasis[d,n,x]BernsteinBasis[4, 3, 0.5]