Additional Results

Abstract

In 1898 the physicist A. Michaelson, by means of a mechanical instrument, tried to draw graphs of the partial sums (up to the eightieth term) of the Fourier series of a real function f. He observed that if, for example, f is a 2π-periodic sawtooth function, the graph of the partial sum s _n , for large n, does not behave as expected near a jump of f. At a downward jump of f the graph of instead of attaching itself closely to the graph of f until very near the jump and then steeply going downwards, starts to oscillate before diving down. An explanation of this phenomenon was discovered and explained already earlier by H. Wilbraham (1848), but this was forgotten for a long time.