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For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

The least common denominator of a collection of fractions (p_1)/(q_1),...,(p_n)/(q_n) is the least common multiple LCM(q_1,...,q_n) of their denominators.

Bourque and Ligh (1992) conjectured that the least common multiple matrix on a GCD-closed set S is nonsingular. This conjecture was shown to be false by Haukkanen et al. ...

The order-n dipole graph D_n is a multigraph consisting of two vertices and n multiple edges joining them. The dipole graph D_2 is a multigraph that can be considered to ...

A loop of an graph is degenerate edge that joins a vertex to itself, also called a self-loop. A simple graph cannot contain any loops, but a pseudograph can contain both ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...

A triple integral is a three-fold multiple integral of the form intintintf(x,y,z)dxdydz. Triple integrals arise in evaluating quantities such as the mass, volume, moment, ...

The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. For a single discrete variable, it is defined by <f(x)>=sum_(x)f(x)P(x), (1) where P(x) ...

A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...