analytic function
121Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …
122Chebyshev cube root — In mathematics, in the theory of special functions, the Chebyshev cube root is a particular inverse function of the Chebyshev polynomial of third degree. It is analogous to the cube root function is the inverse of the third power. It can be used… …
123Laplace's equation — In mathematics, Laplace s equation is a partial differential equation named after Pierre Simon Laplace who first studied its properties. The solutions of Laplace s equation are important in many fields of science, notably the fields of… …
124Hilbert transform — In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u ( t ), and produces a function, H ( u )( t ), with the same domain. The Hilbert transform is named after David Hilbert, who first… …
125Dirichlet series — In mathematics, a Dirichlet series is any series of the form where s and an are complex numbers and n = 1, 2, 3, ... . It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in analytic number theory …
126Hartogs' extension theorem — In mathematics, precisely in the theory of functions of several complex variables, Hartogs extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that the support of the… …
127Cauchy-Riemann equations — In mathematics, the Cauchy Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, are two partial differential equations which provide a necessary and sufficient condition for a differentiable… …
128Bounded mean oscillation — In harmonic analysis, a function of bounded mean oscillation, also known as a BMO function, is a real valued function whose mean oscillation is bounded (finite). The space of functions of bounded mean oscillation (BMO), is a function space that,… …
