Abstract:
In 1885, when Karl Weierstrass was 70 years old, fortunate enough to discover very important and profound theorem: every function continuous on the segment may be approximate arbitrarily near by polynomial of sufficiently great degree. In his article K. Weierstrass expressed hope that the young mathematicians will find explicit formulae for approximate polynomial. In the sequel Lebesgue, Fejér, La Vallée Poussin, Landau and S. Bernstein discovered a set of new original formulas and proofs.
We shall discuss 8-year path which led S.Bernstein (1880-1968) to the invention of polynomials of a very simple structure by his name. By means of this polynomials S. Bernstein gave his famous brief explicit proof of Weierstrass` theorem which was found on probability theory.
