NUMERICAL RESULTS ON BEST UNIFORM RATIONAL APPROXIMATION OF $ \vert x\vert$ ON $ \lbrack-1,\,+1\rbrack$

Abstract

With denoting the error of best uniform rational approximation from to on , we determine the numbers , where each of these numbers was calculated with a precision of at least 200 significant digits. With these numbers, the Richardson extrapolation method was applied to the products , and it appears, to at least 10 significant digits, that which gives rise to an interesting new conjecture in the theory of rational approximation.