@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-BLP2HLSP-6
  skos:prefLabel "calcul intégral"@fr, "integral calculus"@en ;
  a skos:Concept ;
  skos:narrower psr:-V27F12ZJ-1 .

psr:-VZ83B143-L
  skos:prefLabel "fonction hypergéométrique"@fr, "hypergeometric function"@en ;
  a skos:Concept ;
  skos:narrower psr:-V27F12ZJ-1 .

psr:-V27F12ZJ-1
  skos:broader psr:-JXHC9RBH-S, psr:-BLP2HLSP-6, psr:-ZHPKGFBV-J, psr:-VZ83B143-L ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Elliptic_integral>, <https://fr.wikipedia.org/wiki/Int%C3%A9grale_elliptique> ;
  skos:prefLabel "intégrale elliptique"@fr, "elliptic integral"@en ;
  dc:modified "2023-08-17"^^xsd:date ;
  a skos:Concept ;
  skos:definition """In integral calculus, an <b>elliptic integral</b> is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1750</span>). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse. 
<br/>Modern mathematics defines an "elliptic integral" as any function <span class="texhtml"><i>f</i></span> which can be expressed in the form
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle f(x)=\\\\int _{c}^{x}R{\\\\left({\\	extstyle t,{\\\\sqrt {P(t)}}}\\
ight)}\\\\,dt,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>f</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <msubsup>
<br/>          <mo>∫<!-- ∫ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>c</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>x</mi>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mi>R</mi>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow>
<br/>            <mo>(</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mstyle displaystyle="false" scriptlevel="0">
<br/>                <mi>t</mi>
<br/>                <mo>,</mo>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <msqrt>
<br/>                    <mi>P</mi>
<br/>                    <mo stretchy="false">(</mo>
<br/>                    <mi>t</mi>
<br/>                    <mo stretchy="false">)</mo>
<br/>                  </msqrt>
<br/>                </mrow>
<br/>              </mstyle>
<br/>            </mrow>
<br/>            <mo>)</mo>
<br/>          </mrow>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mi>d</mi>
<br/>        <mi>t</mi>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle f(x)=\\\\int _{c}^{x}R{\\\\left({\\	extstyle t,{\\\\sqrt {P(t)}}}\\
ight)}\\\\,dt,}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc8899bb757ea36132340346c8ce30eeecf471de" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -2.338ex; width:27.115ex; height:5.843ex;" alt="{\\\\displaystyle f(x)=\\\\int _{c}^{x}R{\\\\left({\\	extstyle t,{\\\\sqrt {P(t)}}}\\
ight)}\\\\,dt,}"></div>
<br/>where <span class="texhtml"><i>R</i></span> is a rational function of its two arguments, <span class="texhtml"><i>P</i></span> is a polynomial of degree 3 or 4 with no repeated roots, and <span class="texhtml"><i>c</i></span> is a constant. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Elliptic_integral">https://en.wikipedia.org/wiki/Elliptic_integral</a>)"""@en, """Les intégrales elliptiques interviennent dans de nombreux problèmes de physique mathématique : comme par exemple, le calcul de la période d'un pendule aux grandes amplitudes et plus généralement les formes d'équilibre ellipsoïdales des corps en rotation autour d'un axe (planètes, étoiles, goutte d'eau, noyau atomique,...). 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Int%C3%A9grale_elliptique">https://fr.wikipedia.org/wiki/Int%C3%A9grale_elliptique</a>)"""@fr .

psr:-ZHPKGFBV-J
  skos:prefLabel "fonction elliptique"@fr, "elliptic function"@en ;
  a skos:Concept ;
  skos:narrower psr:-V27F12ZJ-1 .

psr: a skos:ConceptScheme .
psr:-JXHC9RBH-S
  skos:prefLabel "elliptic curve"@en, "courbe elliptique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-V27F12ZJ-1 .