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Lemniscate elliptic functions

In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others.

Measurement, Argument identities & Relation to geometric shapes

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Overview

Lemniscate sine and cosine functions

Argument identities

Relation to geometric shapes

Series Identities

Relation to other functions

Inverse functions

Hyperbolic lemniscate functions

Number theory

World map projections

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Lemniscate elliptic functions

Nodes148
Edges147
Triples12
Avg. degree1.99
Density0.013514
Components1

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Lemniscate elliptic functions

Top relations

related to Arc length of Bernoulli's lemniscate · 6
Lemniscate elliptic functions → Angular, APB-APB, Bernoulli, Given, It, Then
related to Elliptic characterization · 5
Lemniscate elliptic functions → BAC, BD, If, Let, The

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Important terminology

displaystyle lemniscate functions operatorname sl varpi elliptic function sine hyperbolic square also mathbb cosine lattice complex cl numbers tfrac length

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
slhinstance ofso the values below0.80text
Lemniscate elliptic functionsrelated to Arc length of Bernoulli's lemniscateBernoulli0.60section
Lemniscate elliptic functionsrelated to Arc length of Bernoulli's lemniscateIt0.60section
Lemniscate elliptic functionsrelated to Arc length of Bernoulli's lemniscateAngular0.60section
Lemniscate elliptic functionsrelated to Arc length of Bernoulli's lemniscateGiven0.60section
Lemniscate elliptic functionsrelated to Arc length of Bernoulli's lemniscateThen0.60section
Lemniscate elliptic functionsrelated to Arc length of Bernoulli's lemniscateAPB-APB0.60section
Lemniscate elliptic functionsrelated to Elliptic characterizationLet0.60section
Lemniscate elliptic functionsrelated to Elliptic characterizationThe0.60section
Lemniscate elliptic functionsrelated to Elliptic characterizationBAC0.60section
Lemniscate elliptic functionsrelated to Elliptic characterizationBD0.60section
Lemniscate elliptic functionsrelated to Elliptic characterizationIf0.60section

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