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Let X be a set of v>=3 elements together with a set B of 3-subset (triples) of X such that every 2-subset of X occurs in exactly one triple of B. Then B is called a Steiner ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

The asymptotic series for the gamma function is given by (1) (OEIS A001163 and A001164). The coefficient a_n of z^(-n) can given explicitly by ...

A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

The tangential triangle is the triangle DeltaT_AT_BT_C formed by the lines tangent to the circumcircle of a given triangle DeltaABC at its vertices. It is therefore antipedal ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...

Iff p is a prime, then (p-1)!+1 is a multiple of p, that is (p-1)!=-1 (mod p). (1) This theorem was proposed by John Wilson and published by Waring (1770), although it was ...

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...