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The inverse trigonometric functions are the inverse functions of the trigonometric functions, written cos^(-1)z, cot^(-1)z, csc^(-1)z, sec^(-1)z, sin^(-1)z, and tan^(-1)z. ...

There are six Painlevé transcendents, corresponding to second-order ordinary differential equations whose only movable singularities are ordinary poles and which cannot be ...

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

Let F(n,sigma) denote the number of permutations on the symmetric group S_n which avoid sigma in S_k as a subpattern, where "tau contains sigma as a subpattern" is ...

The Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans. A technique for using Radon transforms to reconstruct a map of ...

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. It is also the uniform polyhedron with ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...