Bernstein Power Series
- 1 January 1964
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 16, 241-252
- https://doi.org/10.4153/cjm-1964-023-1
Abstract
In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomials are constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalizations of them have appeared. It is our purpose here to consider several generalizations in the form of infinite series and to establish some of their properties.Keywords
This publication has 3 references indexed in Scilit:
- Bernsteinsche PotenzreihenStudia Mathematica, 1960
- On Numerical ApproximationPhysics Today, 1959
- Generalization of Bernstein's polynomials to the infinite intervalJournal of Research of the National Bureau of Standards, 1950