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In many computer languages (such as FORTRAN or the Wolfram Language), the common residue of b (mod m) is written mod(b, m) (FORTRAN) or Mod[b, m] (Wolfram Language). The ...

Let a spherical triangle have sides a, b, and c with A, B, and C the corresponding opposite angles. Then (sin[1/2(A-B)])/(sin[1/2(A+B)]) = (tan[1/2(a-b)])/(tan(1/2c)) (1) ...

Let generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z] (1) have p=q+1. Then the generalized hypergeometric function is said to ...

There are several meanings of "null vector" in mathematics. 1. The most common meaning of null vector is the n-dimensional vector 0 of length 0. i.e., the vector with n ...

A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively ...

There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...

The omega constant is defined as W(1)=0.5671432904... (1) (OEIS A030178), where W(x) is the Lambert W-function. It is available in the Wolfram Language using the function ...

The orthographic projection is a projection from infinity that preserves neither area nor angle. It is given by x = cosphisin(lambda-lambda_0) (1) y = ...

A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if f(x)=f(x+np) for ...

Let p={a_1,a_2,...,a_n} be a permutation. Then i is a permutation ascent if a_i<a_(i+1). For example, the permutation {1,2,3,4} is composed of three ascents, namely {1,2}, ...