@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:-VZ83B143-L
  skos:prefLabel "fonction hypergéométrique"@fr, "hypergeometric function"@en ;
  a skos:Concept ;
  skos:narrower psr:-Q321G8F8-C .

psr:-Q321G8F8-C
  skos:broader psr:-N2QX9K1Z-L, psr:-VZ83B143-L, psr:-B373Q2P1-V ;
  dc:modified "2023-08-16"^^xsd:date ;
  skos:definition """En mathématiques et en physique théorique, les <b>polynômes de Legendre</b> constituent l'exemple le plus simple d'une suite de polynômes orthogonaux. Ce sont des solutions polynomiales <span class="texhtml"><i>P<sub>n</sub></i>(<i>x</i>)</span>, sur l'intervalle <span class="texhtml"><i>x</i> ∈ [–1, 1]</span>, de l'équation différentielle de Legendre&nbsp;:
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\rac {\\\\mathrm {d} }{\\\\mathrm {d} x}}\\\\left[(1-x^{2}){\\rac {\\\\mathrm {d} }{\\\\mathrm {d} x}}P_{n}(x)\\
ight]+n(n+1)\\\\,P_{n}(x)=0}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mi mathvariant="normal">d</mi>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi mathvariant="normal">d</mi>
<br/>              </mrow>
<br/>              <mi>x</mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mrow>
<br/>          <mo>[</mo>
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<br/>            <mo stretchy="false">(</mo>
<br/>            <mn>1</mn>
<br/>            <mo>−<!-- − --></mo>
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<br/>              <mi>x</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
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<br/>            <mo stretchy="false">)</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi mathvariant="normal">d</mi>
<br/>                </mrow>
<br/>                <mrow>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi mathvariant="normal">d</mi>
<br/>                  </mrow>
<br/>                  <mi>x</mi>
<br/>                </mrow>
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<br/>            </mrow>
<br/>            <msub>
<br/>              <mi>P</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>n</mi>
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<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>x</mi>
<br/>            <mo stretchy="false">)</mo>
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<br/>          <mo>]</mo>
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<br/>        <mo>+</mo>
<br/>        <mi>n</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>n</mi>
<br/>        <mo>+</mo>
<br/>        <mn>1</mn>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <msub>
<br/>          <mi>P</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
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<br/>        <mo stretchy="false">(</mo>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {\\\\mathrm {d} }{\\\\mathrm {d} x}}\\\\left[(1-x^{2}){\\rac {\\\\mathrm {d} }{\\\\mathrm {d} x}}P_{n}(x)\\
ight]+n(n+1)\\\\,P_{n}(x)=0}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca5abe3da4707a5253fdff65fa1a417cf778c7b3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:45.744ex; height:6.176ex;" alt="{\\\\displaystyle {\\rac {\\\\mathrm {d} }{\\\\mathrm {d} x}}\\\\left[(1-x^{2}){\\rac {\\\\mathrm {d} }{\\\\mathrm {d} x}}P_{n}(x)\\
ight]+n(n+1)\\\\,P_{n}(x)=0}"></span>,</dd></dl>
<br/>dans le cas particulier où le paramètre <span class="texhtml mvar" style="font-style:italic;">n</span> est un entier naturel. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Polyn%C3%B4me_de_Legendre">https://fr.wikipedia.org/wiki/Polyn%C3%B4me_de_Legendre</a>)"""@fr, """In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">https://en.wikipedia.org/wiki/Legendre_polynomials</a>)"""@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Legendre_polynomials>, <https://fr.wikipedia.org/wiki/Polyn%C3%B4me_de_Legendre> ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:prefLabel "polynôme de Legendre"@fr, "Legendre polynomial"@en .

psr:-N2QX9K1Z-L
  skos:prefLabel "orthogonal polynomials"@en, "polynômes orthogonaux"@fr ;
  a skos:Concept ;
  skos:narrower psr:-Q321G8F8-C .

psr: a skos:ConceptScheme .
psr:-B373Q2P1-V
  skos:prefLabel "combinatorics"@en, "combinatoire"@fr ;
  a skos:Concept ;
  skos:narrower psr:-Q321G8F8-C .