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Given a Poisson distribution with rate of change lambda, the distribution of waiting times between successive changes (with k=0) is D(x) = P(X<=x) (1) = 1-P(X>x) (2) = ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture (Kaplan and ...

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. The probability density function and cumulative ...

There are two definitions of Bernoulli polynomials in use. The nth Bernoulli polynomial is denoted here by B_n(x) (Abramowitz and Stegun 1972), and the archaic form of the ...

The Delta-variation is a variation in which the varied path over which an integral is evaluated may end at different times than the correct path, and there may be variation ...

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic ...

The Gregory series is a pi formula found by Gregory and Leibniz and obtained by plugging x=1 into the Leibniz series, pi/4=sum_(k=1)^infty((-1)^(k+1))/(2k-1)=1-1/3+1/5-... ...

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

The tangent numbers, also called a zag number, and given by T_n=(2^(2n)(2^(2n)-1)|B_(2n)|)/(2n), (1) where B_n is a Bernoulli number, are numbers that can be defined either ...