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The Hilbert transform (and its inverse) are the integral transform g(y) = H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y) (1) f(x) = ...

The symbol ker has at least two different meanings in mathematics. It can refer to a special function related to Bessel functions, or (written either with a capital or ...

Given a set X, a set function mu^*:2^X->[0,infty] is said to be an outer measure provided that mu^*(emptyset)=0 and that mu^* is countably monotone, where emptyset is the ...

The distribution with probability density function and distribution function P(r) = (re^(-r^2/(2s^2)))/(s^2) (1) D(r) = 1-e^(-r^2/(2s^2)) (2) for r in [0,infty) and parameter ...

The word weight has many uses in mathematics. It can refer to a function w(x) (also called a weighting function or weighting function) used to normalize orthogonal functions. ...

The Zipf distribution, sometimes referred to as the zeta distribution, is a discrete distribution commonly used in linguistics, insurance, and the modelling of rare events. ...

The symbol ker has at least two different meanings in mathematics. It can refer to a special function related to Bessel functions, or (written either with a capital or ...

Let E_1(x) be the En-function with n=1, E_1(x) = int_1^infty(e^(-tx)dt)/t (1) = int_x^infty(e^(-u)du)/u. (2) Then define the exponential integral Ei(x) by E_1(x)=-Ei(-x), (3) ...

The variable phi (also denoted am(u,k)) used in elliptic functions and elliptic integrals is called the amplitude (or Jacobi amplitude). It can be defined by phi = am(u,k) ...

The Hadamard product is a representation for the Riemann zeta function zeta(s) as a product over its nontrivial zeros rho, ...