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When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

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 Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" ...

A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ...

The following integral transform relationship, known as the Abel transform, exists between two functions f(x) and g(t) for 0<alpha<1, f(x) = int_0^x(g(t)dt)/((x-t)^alpha) (1) ...

An Archimedean spiral is a spiral with polar equation r=atheta^(1/n), (1) where r is the radial distance, theta is the polar angle, and n is a constant which determines how ...

Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...

A bitangent is a line that is tangent to a curve at two distinct points. Aa general plane quartic curve has 28 bitangents in the complex projective plane. However, as shown ...

The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes ...