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Analytic function

In mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at a point if, in some neighborhood of that point, it is equal to a power series centered there. The analytic function is therefore locally determined by coefficients of the series…

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Overview

Definitions

Examples

Alternative characterizations

Properties of analytic functions

Analyticity and differentiability

Real versus complex analytic functions

Taylor series and radius of convergence

Analytic continuation

Analytic functions of several variables

Analytic functions over other valued fields

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Analytic function

Nodes102
Edges101
Triples98
Avg. degree1.98
Density0.019608
Components1

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Analytic function

Top relations

related to References · 19
Analytic function → Birkhäuser, Complex Analysis, Conway, Functions, Gamelin, Graduate Texts, Harold, ISBN, John, Krantz, Mathematics, One Complex Variable, Parks, Primer, Real Analytic Functions, Springer, Springer-Verlag, Steven, Theodore
related to Examples · 13
Analytic function → Algebraic, All, Any Taylor, Furthermore, Maclaurin, Many, Near, Power, Puiseux, Riemann, Taylor, The, Typical
related to Properties of analytic functions · 13
Analytic function → Analyticity, Any, Banach, For, Fréchet, If, In, Jacobian, Morera's, Omega, Real, The, This
related to Analytic functions of several variables · 10
Analytic function → Analytic, Domains, Hartogs's, However, In, One, Power, The, This, Zero
related to External links · 10
Analytic function → Analytic, EMS Press, Encyclopedia, Eric, Ivan, Ivanov, Mathematics, MathWorld, Solver, Weisstein
related to Analyticity and differentiability · 7
Analytic function → Any, As, Consequently, In, Non-analytic, The, There
related to Analytic functions over other valued fields · 6
Analytic function → Analogous, Analytic, Archimedean, If, In, Laurent
related to Analytic continuation · 5
Analytic function → Analytic, Because, More, Starting, This
related to Real versus complex analytic functions · 5
Analytic function → According, Analyticity, Liouville's, Real, The
related to Definitions · 4
Analytic function → Alternatively, Formally, Taylor, The

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Important terminology

analytic function series displaystyle complex functions real open power point set convergent convergence holomorphic taylor domain converges neighborhood infty smooth

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Analytic functionis afunction that is locally represented by a convergent power series0.90text
Analytic functionis afunction that is locally represented by a convergent Taylor series.Analytic functions occur in both real analysis and complex analysis0.90text
Analytic functionis ainfinitely differentiable function such that the Taylor series at each point x 00.90text
Analytic functionrelated to Analytic continuationBecause0.60section
Analytic functionrelated to Analytic continuationThis0.60section
Analytic functionrelated to Analytic continuationStarting0.60section
Analytic functionrelated to Analytic continuationAnalytic0.60section
Analytic functionrelated to Analytic continuationMore0.60section
Analytic functionrelated to Analytic functions of several variablesOne0.60section
Analytic functionrelated to Analytic functions of several variablesPower0.60section
Analytic functionrelated to Analytic functions of several variablesAnalytic0.60section
Analytic functionrelated to Analytic functions of several variablesHowever0.60section

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