Bernstein's constant

Bernstein's constant, usually denoted by the Greek letter β, is a mathematical constant named after Sergei Natanovich Bernstein and is equal to 0.2801694990....

Definition

Let E_n be the error of the best uniform approximation to a real function ƒ on the interval by real polynomials of no more than degree n. In the case of ƒ = |x|, Bernstein showed that the limit
called Bernstein's constant, exists and is between 0.278 and 0.286. His conjecture that the limit is:
was disproven by Varga and Carpenter, who calculated