An Euler-Fourier series and the Wilbraham-Gibbs phenomenon. (Una serie di Eulero - Fourier e il fenomeno di Wilbraham - Gibbs.) (Italian)

Lett. mat. Pristem, No. 26, 27-34 (1997).

The author discusses from a mathematical and historical point of view Wilbraham-Gibbs phenomenon, namely the fact that if we write the Fourier series of any “reasonable” locally integrable function, with period $2π$, the series converges in every point ‒ but if we take a function with a jump, in a neighbourhood of the discontinuity the partial sums of the Fourier series have fast oscillations and “miss the target” by approximately 9\% of the value of the jump.