Bernstein's constant
| Binary | 0.01000111101110010011000000110011… |
| Decimal | 0.280169499… |
| Hexadecimal | 0.47B930338AAD… |
| Continued fraction |
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 En 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|, showed that the limitcalled Bernstein's constant, exists and is between 0.278 and 0.286. His conjecture that the limit is:
was disproven by, who calculated