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Jacobi elliptic functions

In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic…

Measurement, Overview & Definition in terms of inverses of elliptic integrals

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Overview

Notation

Definition in terms of inverses of elliptic integrals

Definition as trigonometry: the Jacobi ellipse

Definition in terms of the Jacobi theta functions

Definition in terms of Neville theta functions

Jacobi transformations

The Jacobi hyperbola

Periodicity, poles, and residues

Special values

Identities

Jacobi elliptic functions as solutions of nonlinear ordinary differential equations

Expansion in terms of the nome

Fast computation

Continued fractions

Inverse functions

Map projection

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Jacobi elliptic functions

Nodes80
Edges79
Triples61
Avg. degree1.98
Density0.025
Components1

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Jacobi elliptic functions

Top relations

related to Fast computation · 10
Jacobi elliptic functions → Define, If, Initialize, It, Jacobi, Landen's, The, Then, There, This
related to Notation · 9
Jacobi elliptic functions → Elliptic, Functions, Glaisher, Gudermann, Jacobi, Jacobi's, The, These, This
related to Using modular inversion · 9
Jacobi elliptic functions → Also, Cox, In, Jacobi, Re, The, Then Whittaker, Watson, Whittaker
related to overview · 8
Jacobi elliptic functions → As, Depending, Functions, However, In, Jacobi, The, There
related to External links · 7
Jacobi elliptic functions → EMS Press, Encyclopedia, Eric, Jacobi, Mathematics, MathWorld, Weisstein
related to Periodicity, poles, and residues · 5
Jacobi elliptic functions → Each, For, In, Jacobi, The
related to Definition as trigonometry: the Jacobi ellipse · 3
Jacobi elliptic functions → Jacobi, Let, Similarly
related to Derivatives with respect to the first variable · 3
Jacobi elliptic functions → Jacobi, The, These
related to Inverse functions · 3
Jacobi elliptic functions → Jacobi, The, They
related to Approximation in terms of hyperbolic functions · 2
Jacobi elliptic functions → The Jacobi, When

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displaystyle operatorname functions elliptic jacobi frac sn dn cn function sin sqrt mathrm 1-m mathbb pq complex real poles varphi

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Jacobi elliptic functionsrelated to Approximation in terms of hyperbolic functionsThe Jacobi0.60section
Jacobi elliptic functionsrelated to Approximation in terms of hyperbolic functionsWhen0.60section
Jacobi elliptic functionsrelated to Definition as trigonometry: the Jacobi ellipseSimilarly0.60section
Jacobi elliptic functionsrelated to Definition as trigonometry: the Jacobi ellipseJacobi0.60section
Jacobi elliptic functionsrelated to Definition as trigonometry: the Jacobi ellipseLet0.60section
Jacobi elliptic functionsrelated to Definition in terms of Neville theta functionsThe Jacobi0.60section
Jacobi elliptic functionsrelated to Definition in terms of Neville theta functionsNeville0.60section
Jacobi elliptic functionsrelated to Derivatives with respect to the first variableThe0.60section
Jacobi elliptic functionsrelated to Derivatives with respect to the first variableJacobi0.60section
Jacobi elliptic functionsrelated to Derivatives with respect to the first variableThese0.60section
Jacobi elliptic functionsrelated to External linksJacobi0.60section
Jacobi elliptic functionsrelated to External linksEncyclopedia0.60section

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