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Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation that initially defined the function becomes divergent.

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Overview

Initial discussion

Applications

Worked example

Formal definition of a germ

The topology of the set of germs

Examples of analytic continuation

Natural boundary

Monodromy theorem

Hadamard's gap theorem

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Analytic continuation

Nodes73
Edges72
Triples31
Avg. degree1.97
Density0.027397
Components1

How this topic connects Entity context

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Analytic continuation

Top relations

related to External links · 7
Analytic continuation → Analytic, EMS Press, Encyclopedia, Eric, Mathematics, MathPagesWeisstein, MathWorld
related to Example I: A function with a natural boundary at zero (the prime zeta function) · 5
Analytic continuation → For, Re, Riemann, The, This
related to The topology of the set of germs · 5
Analytic continuation → If, Let, The, This, We
has application · 3
Analytic continuation → Examples, In, Riemann
related to Formal definition of a germ · 3
Analytic continuation → Dr, Let, The
related to Initial discussion · 3
Analytic continuation → If, In, Suppose
related to Monodromy theorem · 3
Analytic continuation → If, Suppose, The
is a · 1
Analytic continuation → technique to extend the domain of definition of a given analytic function
see also · 1
Analytic continuation → Mittag-Leffler

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Important terminology

displaystyle analytic function continuation series power complex mathcal domain sheaf set natural boundary germ open convergence defined circle theorem mathbb

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Analytic continuationis atechnique to extend the domain of definition of a given analytic function0.90text
Analytic continuationhas applicationIn0.60section
Analytic continuationhas applicationExamples0.60section
Analytic continuationhas applicationRiemann0.60section
Analytic continuationrelated to Example I: A function with a natural boundary at zero (the prime zeta function)For0.60section
Analytic continuationrelated to Example I: A function with a natural boundary at zero (the prime zeta function)Re0.60section
Analytic continuationrelated to Example I: A function with a natural boundary at zero (the prime zeta function)This0.60section
Analytic continuationrelated to Example I: A function with a natural boundary at zero (the prime zeta function)Riemann0.60section
Analytic continuationrelated to Example I: A function with a natural boundary at zero (the prime zeta function)The0.60section
Analytic continuationrelated to External linksAnalytic0.60section
Analytic continuationrelated to External linksEncyclopedia0.60section
Analytic continuationrelated to External linksMathematics0.60section

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