Gibbs Phenomenon

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An overshoot of Fourier Series and other Eigenfunction series occurring at simple Discontinuities. It can be removed with the Lanczos Sigma Factor.

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.