A Limit Function for Equidistant Fourier Interpolation

Denote by s_n the nth order Fourier polynomial of the odd function f of period 2π equal to 1 on ]0, π. The Gibbs phenomenon is caused by the well-known fact that formula] An analogous Gibbs phenomenon is caused by a similar limiting behaviour of s*_n, the nth order trigonometric polynomial interpolating f at jπ/n (1 ≤ j ≤ 2n).