Communications of the
Korean Mathematical Society CKMS

The Fourier series has a rapid oscillation near end points at jump discontinuity which is called the Gibbs phenomenon. There is an overshoot (or undershoot) of approximately 9\% at jump discontinuity. In this paper, we prove that a bunch of series representations (certain nonharmonic Fourier series) give good approximations vanishing Gibbs phenomenon. Also we have an application for approximating some shape of upper part of a vehicle in a different way from the method of cubic splines and wavelets.

Keywords: Gibbs phenomenon, certain nonharmonic Fourier series, splines and wavelets

MSC numbers: 42A20, 42A24