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Category:Complex analysis
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{{commonscat|Complex analysis}} {{Wiktionary}} '''[[Complex analysis]]''' is the branch of [[mathematics]] investigating [[holomorphic function]]s, i.e. functions which are defined in some region of the [[complex number|complex plane]], take complex values, and are differentiable as complex functions. Complex differentiability has much stronger consequences than usual (real) [[derivative|differentiability]]. For instance, every holomorphic function is representable as [[power series]] in every open disc in its domain of definition, and is therefore [[analytic function|analytic]]. In particular, holomorphic functions are infinitely differentiable, a fact that is far from true for real differentiable functions. Most elementary functions, such as all [[polynomial]]s, the [[exponential function]], and the [[trigonometric function]]s, are holomorphic. See also : [[Holomorphic sheaf|holomorphic sheaves]] and [[vector bundle]]s. [[Category:Fields of mathematical analysis]] {{CatAutoTOC}}
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