Search Results for ""

Denoted zn(u,k) or Z(u). Z(phi|m)=E(phi|m)-(E(m)F(phi|m))/(K(m)), where phi is the Jacobi amplitude, m is the parameter, and F(phi|m) and K(m) are elliptic integrals of the ...

The Maxwell (or Maxwell-Boltzmann) distribution gives the distribution of speeds of molecules in thermal equilibrium as given by statistical mechanics. Defining a=sqrt(kT/m), ...

The bivariate normal distribution is the statistical distribution with probability density function P(x_1,x_2)=1/(2pisigma_1sigma_2sqrt(1-rho^2))exp[-z/(2(1-rho^2))], (1) ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing ...

The distribution function D(x), also called the cumulative distribution function (CDF) or cumulative frequency function, describes the probability that a variate X takes on a ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...

Let the elliptic modulus k satisfy 0<k^2<1. (This may also be written in terms of the parameter m=k^2 or modular angle alpha=sin^(-1)k.) The incomplete elliptic integral of ...