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The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

The operator representing the computation of a derivative, D^~=d/(dx), (1) sometimes also called the Newton-Leibniz operator. The second derivative is then denoted D^~^2, the ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D and which is invariant under a countably infinite group of ...

The symbol RadicalBox[x, n] used to indicate a root is called a radical, or sometimes a surd. The expression RadicalBox[x, n] is therefore read "x radical n," or "the nth ...

A solution to the spherical Bessel differential equation. The two types of solutions are denoted j_n(x) (spherical Bessel function of the first kind) or n_n(x) (spherical ...

A shortened term for integral transform. Geometrically, if S and T are two transformations, then the similarity transformation TST^(-1) is sometimes called the transform ...

Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) = 2/pisin^(-1)[sin(pix)] (1) = 1-2|1-[2(1/2x+1/4 (mod 1))]| (2) = ...

The box fractal is a fractal also called the anticross-stitch curve which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 0 ...