The dual basis functions for the Bernstein polynomials
The Bernstein polynomials \(B^n_i\), \(i=0,1,\dots,n\) form a basis of the \((n+1)\)-dimensional real linear space \(P^n\) of all polynomials of maximal degree \(n\). The dual basis functions \(D^n_j\) with respect to the inner product of \(L^2[0,1]\) can be represented as linear combinations of the \(B^n_i\). The paper under review gives an explicit representation of the coefficients of these linear combinations in terms of products of binomial coefficients.
scientific article; zbMATH DE number 1187657