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A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function ...

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

The Fourier transform of the constant function f(x)=1 is given by F_x[1](k) = int_(-infty)^inftye^(-2piikx)dx (1) = delta(k), (2) according to the definition of the delta ...

The singular support of a generalized function u is the complement of the largest open set on which u is smooth. Roughly speaking, it is the closed set where the distribution ...

The inverse of the Laplace transform, given by F(t)=1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds, where gamma is a vertical contour in the complex plane chosen so ...

Let Gamma be a representation for a group of group order h, then sum_(R)Gamma_i(R)_(mn)Gamma_j(R)_(m^'n^')^*=h/(sqrt(l_il_j))delta_(ij)delta_(mm^')delta_(nn^'). The proof is ...

The function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

The Hofstadter ellipses are a family of triangle ellipses introduced by P. Moses in February 2005. The Hofstadter ellipse E(r) for parameter 0<r<1 is defined by the trilinear ...

The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...