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The Gibbs phenomenon is an overshoot (or "ringing") of Fourier series and other eigenfunction series occurring at simple discontinuities. It can be reduced with the Lanczos ...

Let K subset= C be compact, let f be analytic on a neighborhood of K, and let P subset= C^*\K contain at least one point from each connected component of C^*\K. Then for any ...

A method of numerically integrating ordinary differential equations by using a trial step at the midpoint of an interval to cancel out lower-order error terms. The ...

The asymptotic series of the Airy function Ai(z) (and other similar functions) has a different form in different sectors of the complex plane.

The appearance of nontrivial zeros (i.e., those along the critical strip with R[z]=1/2) of the Riemann zeta function zeta(z) very close together. An example is the pair of ...

A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite ...

A sampling phenomenon produced when a waveform is not sampled uniformly at an interval t each time, but rather at a series of slightly shifted intervals t+Deltat_i such that ...

Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater ...

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...