ON THE KHINTCHINE CONSTANT

We present rapidly converging series for tile Khintchine constant and for general ''Khintchine means'' of continued. fractions, We show that each of these constants can be cast in terms of an efficient free-par ameter series, each series involving values of the Riemann zeta functi on, rationals, and logarithms of rationals. We provide an alternative, polylogarithm series for the Khintchine constant and indicate means t o accelerate such series. We discuss properties of some explicit conti nued fractions, constructing specific fractions that have limiting geo metric mean equal to the Khintchine constant. We report numerical eval uations of such special numbers and of various Khintchine means. In pa rticular, we used an optimized series and a collection of fast algorit hms to evaluate the Khintchine constant to more than 7000 decimal plac es.