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The integral transform (Kf)(x)=int_0^infty((x-t)_+^(c-1))/(Gamma(c))_2F_1(a,b;c;1-t/x)f(t)dt, where Gamma(x) is the gamma function, _2F_1(a,b;c;z) is a hypergeometric ...

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 ...

In order to recover all Fourier components of a periodic waveform, it is necessary to use a sampling rate nu at least twice the highest waveform frequency. The Nyquist ...

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

The ruliad may be defined as the entangled limit of everything that is computationally possible, i.e., the result of following all possible computational rules in all ...

Stanley and Wilf conjectured (Bona 1997, Arratia 1999), that for every permutation pattern sigma, there is a constant c(sigma)<infty such that for all n, ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

A Wilson prime is a prime satisfying W(p)=0 (mod p), where W(p) is the Wilson quotient, or equivalently, (p-1)!=-1 (mod p^2). The first few Wilson primes are 5, 13, and 563 ...