holomorphic

which is complex-differentiable everywhere

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  • holomorphic — 1880, from HOLO (Cf. holo ) + morphic (see METAMORPHOSIS (Cf. metamorphosis)) …   Etymology dictionary

  • holomorphic — [häl΄ōmôr′fik, hō΄ləmôr′fik] adj. [ HOLO + MORPHIC] having the two ends symmetrical in form: said of a crystal …   English World dictionary

  • holomorphic — holomorphism, holomorphy, n. /hol euh mawr fik, hoh leuh /, adj. Math. analytic (def. 5). [1875 80; HOLO + MORPHIC] * * * …   Universalium

  • holomorphic — ho·lo·mor·phic …   English syllables

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

  • 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

  • Holomorphic vector bundle — In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is complex manifold and the projection map pi:E o X is holomorphic.Specifically, one requires that the trivialization… …   Wikipedia

  • Proof that holomorphic functions are analytic — In complex analysis, a field of mathematics, a complex valued function f of a complex variable z *is holomorphic at a point a iff it is differentiable at every point within some open disk centered at a , and* is analytic at a if in some open disk …   Wikipedia

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