Bernstein Expansion

Author

Eric W. Weisstein
December 17, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/BernsteinExpansion.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BernsteinExpansion.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

BernsteinExpansion[n_,f_,x_]:=Sum[Binomial[n,j] x^j (1-x)^(n-j) Function[x,f][j/n],{j,0,n}]

Example

FullSimplify[BernsteinExpansion[n,x,x],n>=0&&n∈Integers]