Bernstein polynomials via the shifting operator. (English) Zbl 0563.41007
The univariate Bernstein polynomial is expressed in terms of the so- called shifting operator which enables us to verify very neatly some fundamental properties of these polynomials. By using Bernstein polynomials, the formula for the sum of pth powers of the first n integers and an explicit expression for the cardinal basis functions of two-point Hermite interpolation are derived.
MSC:
41A10 | Approximation by polynomials |