Bernstein's constant, usually denoted by the Greek letter ò (beta), is a mathematical constant named after Sergei Natanovich Bernstein and is equal to 0.2801694990... .
Let E<sub>n</sub>(ÃÂ) be the error of the best uniform approximation to a real function ÃÂ(x) on the interval [−1, 1] by real polynomials of no more than degree n. In the case of ÃÂ(x) = |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