incomplete elliptic integral of the first kind

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-20.10

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https://metanorma.github.io/isq-smart/math/part-2-20/t2-20.10
urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.10

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-20.10

IEC

urn:iec:std:iec:80000-2:2019:::item:2-20.10

Designations

ENincomplete elliptic integral of the first kind

FRintégrale elliptique incomplète de première espèce

Symbol

F (φ, k)

Notation systems

AsciiMath

"F"(varphi,k)

LaTeX

\text{F} ( \varphi , k )

Definition

incomplete elliptic integral of the first kind

intégrale elliptique incomplète de première espèce

$F (φ, k) = \int_{0}^{φ} \frac{d σ}{\sqrt{1 - k^{2} {sin}^{2} σ}}$

$k \in R$ , $0 < k < 1$

$K (k) = F (\frac{π}{2}, k)$ , is the complete elliptic integral of the first kind.

$F (φ, k) = \int_{0}^{φ} \frac{d σ}{\sqrt{1 - k^{2} {sin}^{2} σ}}$

$k \in R$ , $0 < k < 1$

$K (k) = F (\frac{π}{2}, k)$ , est l'intégrale elliptique complète de première espèce.

A mathematical concept as defined in ISO/IEC 80000 Part 2.

isq:t2-20.10

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-20.10
skosxl:prefLabel	"incomplete elliptic integral of the first kind"@en
skosxl:altLabel	""F"(varphi,k)"@en
skos:definition	incomplete elliptic integral of the first kind
skos:note	stem:["F"(varphi,k) = int_0^varphi ("d"sigma)/(sqrt(1-k^2"sin"^2 sigma))] stem:[k in bb(sf(R))], stem:[0<k<1] stem:["K…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-20