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holomorphic function

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  • Holomorphic function — A rectangular grid (top) and its image under a holomorphic function f (bottom). In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex valued function of one or more complex …   Wikipedia

  • Holomorphic functional calculus — In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function fnof; of a complex argument z and an operator T , the aim is to construct an operator:f(T),which in a… …   Wikipedia

  • Holomorphic sheaf — In mathematics, more specifically complex analysis, a holomorphic sheaf (often also called an analytic sheaf) is a natural generalization of the sheaf of holomorphic functions on a complex manifold. DefinitionIt takes a rather involved string of… …   Wikipedia

  • Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

  • Function space — In mathematics, a function space is a set of functions of a given kind from a set X to a set Y . It is called a space because in many applications, it is a topological space or a vector space or both. ExamplesFunction spaces appear in various… …   Wikipedia

  • holomorphic — ˌhōləˈmȯrfik, ˌhäl adjective Etymology: hol + morphic of a function of a complex variable : analytic 2 herein …   Useful english dictionary

  • Zeta function universality — In mathematics, the universality of zeta functions is the remarkable property of the Riemann zeta function and other, similar, functions, such as the Dirichlet L functions, to approximate arbitrary non vanishing holomorphic functions arbitrarily… …   Wikipedia

  • Meromorphic function — In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function. (The terminology comes from the Ancient Greek meros …   Wikipedia

  • Harmonic function — In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U rarr; R (where U is an open subset of R n ) which satisfies Laplace s equation,… …   Wikipedia

  • Antiholomorphic function — In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions.A function defined on an open set in the complex plane is called antiholomorphic… …   Wikipedia

  • Riemann-Siegel theta function — In mathematics, the Riemann Siegel theta function is defined in terms of the Gamma function as: heta(t) = arg left(Gammaleft(frac{2it+1}{4} ight) ight) frac{log pi}{2} tfor real values of t. Here the argument is chosen in such a way that a… …   Wikipedia

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