These were not the first estimates for E,* but they were the cleanest. Only a year earlier, Lebesguc had given estimates for approximation by the nth Fourier sums; but the latter contain logarithms which are absent in (3). As natural as (3) seems, there is still the question whether it is in some sense best possible. Bernstein [2] showed that this is the case, in at least two different ways. He...
