An overshoot of Fourier Series and other Eigenfunction series occurring at simple Discontinuities. It can be removed with the Lanczos Sigma Factor.
See also Fourier Series
References
Arfken, G. ``Gibbs Phenomenon.'' §14.5 in Mathematical Methods for Physicists, 3rd ed.
Orlando, FL: Academic Press, pp. 783-787, 1985.
Foster, J. and Richards, F. B. ``The Gibbs Phenomenon for Piecewise-Linear Approximation.''
Amer. Math. Monthly 98, 47-49, 1991.
Gibbs, J. W. ``Fourier Series.'' Nature 59, 200 and 606, 1899.
Hewitt, E. and Hewitt, R. ``The Gibbs-Wilbraham Phenomenon: An Episode in Fourier Analysis.''
Arch. Hist. Exact Sci. 21, 129-160, 1980.
Sansone, G. ``Gibbs' Phenomenon.'' §2.10 in Orthogonal Functions, rev. English ed.
New York: Dover, pp. 141-148, 1991.