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A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

A coefficient of the Maclaurin series of 1/(ln(1+x))=1/x+1/2-1/(12)x+1/(24)x^2-(19)/(720)x^3+3/(160)x^4+... (OEIS A002206 and A002207), the multiplicative inverse of the ...

Given a point lattice, a cluster is a group of filled cells which are all connected to their neighbors vertically or horizontally.

A requirement necessary for a given statement or theorem to hold. Also called a criterion.

A recurrence relation between the function Q arising in quota systems, Q(n,r)=Q(n-1,r-1)+Q(n-1,r).

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers ...

Two losing gambling games can be set up so that when they are played one after the other, they become winning. There are many ways to construct such scenarios, the simplest ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...

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 ...

If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as ...