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Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...

Let (X,A,mu) and (Y,B,nu) be measure spaces. A measurable rectangle is a set of the form A×B for A in A and B in B.

A multiple of a number x is any quantity y=nx with n an integer. If x and y are integers, then x is called a factor of y. The smallest positive number m for which there exist ...

When |x|<1/2, (1-x)^(-a)_2F_1(a,b;c;-x/(1-x))=_2F_1(a,c-b;c;x).

The derivative of the power x^n is given by d/(dx)(x^n)=nx^(n-1).

The primitive part of a polynomial P(x) is P(x)/k, where k is the content. For a general univariate polynomial P(x), the Wolfram Language function FactorTermsList[poly, x] ...

The doublestruck capital letter Q, Q, denotes the field of rationals. It derives from the German word Quotient, which can be translated as "ratio." The symbol Q first ...

The derivative rule d/(dx)[(f(x))/(g(x))]=(g(x)f^'(x)-f(x)g^'(x))/([g(x)]^2).

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

Given two distributions Y and X with joint probability density function f(x,y), let U=Y/X be the ratio distribution. Then the distribution function of u is D(u) = P(U<=u) (1) ...