On rational approximation of the exponential and the square root function

Abstract

Fifteen years ago Meinardus made a conjecture on the degree of the rational approximation of the function ex on the interval [−1,+1]. The conjecture was recently proved via the approximation on the circle |z|=½ in the complex plane. The same method is now applied to the approximation of the square root function. Here we have a gap between the upper and the lower bound, the amount of which depends on the location of the branch point. To close the gap some folklore about Heron's method is collected and completed.