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Branch point

In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n {\displaystyle n} -valued (has n {\displaystyle n} values) at that point, all of its neighborhoods contain a point that has more than n {\displaystyle n} values. Multi-valued functions are rigorously studied using Riemann…

Algebraic branch points, Branch cuts & Algebraic geometry

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Overview

Algebraic branch points

Transcendental and logarithmic branch points

Examples

Branch cuts

Riemann surfaces

Algebraic geometry

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Branch point

Nodes54
Edges53
Triples73
Avg. degree1.96
Density0.037037
Components1

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Branch point

Top relations

related to References · 37
Branch point → Ablowitz, Academic Press, Algebraic Geometry, Applications, Applied Mathematics, Athanassios, Berlin, Boston, Branch, Cambridge Texts, Cambridge University Press, Complex Analysis, Complex Variables, EMS Press, Encyclopedia, Englewood Cliffs, Fokas, Introduction, ISBN, MA
related to Algebraic geometry · 8
Branch point → Assume, By, For, In, Let, Pulling, The, Then
related to Examples · 8
Branch point → As, If, In, Since, Suppose, The, This, When
related to Algebraic branch points · 7
Branch point → Equivalently, If, Let, Omega, So, The, This
related to Branch cuts · 4
Branch point → Branch, For, Roughly, The
related to Riemann surfaces · 4
Branch point → For, Riemann, The, Unless
related to Transcendental and logarithmic branch points · 3
Branch point → An, Suppose, Then
is a · 2
Branch point → origin, origin for the multi-valued function g

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Important terminology

branch function point points displaystyle ramification complex around algebraic logarithm cut analytic monodromy one origin transcendental functions logarithmic example along

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Branch pointis aorigin0.90text
Branch pointis aorigin for the multi-valued function g0.90text
Branch pointrelated to Algebraic branch pointsLet0.60section
Branch pointrelated to Algebraic branch pointsOmega0.60section
Branch pointrelated to Algebraic branch pointsIf0.60section
Branch pointrelated to Algebraic branch pointsSo0.60section
Branch pointrelated to Algebraic branch pointsThe0.60section
Branch pointrelated to Algebraic branch pointsEquivalently0.60section
Branch pointrelated to Algebraic branch pointsThis0.60section
Branch pointrelated to Algebraic geometryIn0.60section
Branch pointrelated to Algebraic geometryLet0.60section
Branch pointrelated to Algebraic geometryBy0.60section

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