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Title: Analytic Function -- from Wolfram MathWorld

Open Graph Title: Analytic Function -- from Wolfram MathWorld

X Title: Analytic Function -- from Wolfram MathWorld

Description: A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with "analytic function" (Krantz 1999, p. 16). Many mathematicians prefer the term "holomorphic function" (or "holomorphic map") to "analytic function" (Krantz 1999, p. 16), while "analytic" appears to be in...

Open Graph Description: A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with "analytic function" (Krantz 1999, p. 16). Many mathematicians prefer the term "holomorphic function" (or "holomorphic map") to "analytic function" (Krantz 1999, p. 16), while "analytic" appears to be in...

X Description: A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with "analytic function" (Krantz 1999, p. 16). Many mathematicians prefer the term "holomorphic function" (or "holomorphic map") to "analytic function" (Krantz 1999, p. 16), while "analytic" appears to be in...

Opengraph URL: https://mathworld.wolfram.com/AnalyticFunction.html

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DC.TitleAnalytic Function
DC.CreatorWeisstein, Eric W.
DC.DescriptionA complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with "analytic function" (Krantz 1999, p. 16). Many mathematicians prefer the term "holomorphic function" (or "holomorphic map") to "analytic function" (Krantz 1999, p. 16), while "analytic" appears to be in...
DC.Date.Modified2002-12-17
DC.Subject32
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/AnalyticFunction.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2002-12-17
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complex functionhttps://mathworld.wolfram.com/ComplexFunction.html
complex differentiablehttps://mathworld.wolfram.com/ComplexDifferentiable.html
holomorphic functionhttps://mathworld.wolfram.com/HolomorphicFunction.html
holomorphic functionhttps://mathworld.wolfram.com/HolomorphicFunction.html
complex functionhttps://mathworld.wolfram.com/ComplexFunction.html
differentiablehttps://mathworld.wolfram.com/Differentiable.html
singularitieshttps://mathworld.wolfram.com/Singularity.html
branch cutshttps://mathworld.wolfram.com/BranchCut.html
complex functionhttps://mathworld.wolfram.com/ComplexFunction.html
complex planehttps://mathworld.wolfram.com/ComplexPlane.html
entirehttps://mathworld.wolfram.com/EntireFunction.html
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poleshttps://mathworld.wolfram.com/Pole.html
essential singularitieshttps://mathworld.wolfram.com/EssentialSingularity.html
meromorphic functionhttps://mathworld.wolfram.com/MeromorphicFunction.html
Anti-Analytic Functionhttps://mathworld.wolfram.com/Anti-AnalyticFunction.html
Bergman Spacehttps://mathworld.wolfram.com/BergmanSpace.html
Cauchy-Riemann Equationshttps://mathworld.wolfram.com/Cauchy-RiemannEquations.html
Complex Differentiablehttps://mathworld.wolfram.com/ComplexDifferentiable.html
Complex Functionhttps://mathworld.wolfram.com/ComplexFunction.html
Complex Planehttps://mathworld.wolfram.com/ComplexPlane.html
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Entire Functionhttps://mathworld.wolfram.com/EntireFunction.html
Holomorphic Functionhttps://mathworld.wolfram.com/HolomorphicFunction.html
Meromorphic Functionhttps://mathworld.wolfram.com/MeromorphicFunction.html
Pseudoanalytic Functionhttps://mathworld.wolfram.com/PseudoanalyticFunction.html
Real Analytic Functionhttps://mathworld.wolfram.com/RealAnalyticFunction.html
Regular Functionhttps://mathworld.wolfram.com/RegularFunction.html
Semianalytichttps://mathworld.wolfram.com/Semianalytic.html
Singularityhttps://mathworld.wolfram.com/Singularity.html
Subanalytichttps://mathworld.wolfram.com/Subanalytic.html
Explore this topic in the MathWorld classroomhttps://mathworld.wolfram.com/classroom/AnalyticFunction.html
complex analysis https://www.wolframalpha.com/input/?i=complex+analysis
branch points sqrt(z) https://www.wolframalpha.com/input/?i=branch+points+sqrt%28z%29
branch cuts ln(z) https://www.wolframalpha.com/input/?i=branch+cuts+ln%28z%29
Theory of Functions Parts I and II, Two Volumes Bound as One, Part I.http://www.amazon.com/exec/obidos/ASIN/0486692191/ref=nosim/ericstreasuretro
Handbook of Complex Variables.http://www.amazon.com/exec/obidos/ASIN/0817640118/ref=nosim/ericstreasuretro
Methods of Theoretical Physics, Part I.http://www.amazon.com/exec/obidos/ASIN/007043316X/ref=nosim/ericstreasuretro
A Course in Modern Analysis, 4th ed.http://www.amazon.com/exec/obidos/ASIN/0521091896/ref=nosim/ericstreasuretro
Analytic Functionhttps://www.wolframalpha.com/input/?i=analytic+function
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