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"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

An integer m such that if p|m, then p^2|m, is called a powerful number. There are an infinite number of powerful numbers, and the first few are 1, 4, 8, 9, 16, 25, 27, 32, ...

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x)=a_3x^3+a_2x^2+a_1x+a_0. An equation involving a cubic polynomial is called a ...

A quadratic polynomial is a polynomial of degree 2. A univariate quadratic polynomial has the form f(x)=a_2x^2+a_1x+a_0. An equation involving a quadratic polynomial is ...

A mathematical relationship expressing f_n as some combination of f_i with i<n. When formulated as an equation to be solved, recurrence relations are known as recurrence ...