@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: a skos:ConceptScheme .
psr:-QFN3LTHB-5
  dc:created "2023-07-27"^^xsd:date ;
  a skos:Concept ;
  dc:modified "2023-07-27"^^xsd:date ;
  skos:definition """En mathématiques, les <b>fonctions de Legendre</b>, notées <i>P</i><sub>λ</sub> (première espèce) et <i>Q</i><sub>λ</sub> (seconde espèce), ainsi que les <i>fonctions associées de Legendre</i> correspondantes, notées <i>P</i><span class="unicode" style="white-space:nowrap; display:inline-block; margin-bottom:-0.3em; vertical-align:-0.4em; line-height:1em; font-size:80%; text-align:left;">μ<br>λ</span> et <i>Q</i><span class="unicode" style="white-space:nowrap; display:inline-block; margin-bottom:-0.3em; vertical-align:-0.4em; line-height:1em; font-size:80%; text-align:left;">μ<br>λ</span>, sont des généralisations des polynômes de Legendre <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 P_{\\\\ell }(x)}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>P</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>ℓ<!-- ℓ --></mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle P_{\\\\ell }(x)}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a16bd480e0c257a118bc3a5a33156897b24d3f8" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.549ex; height:2.843ex;" alt="P_{{\\\\ell }}(x)"></span> et des polynômes associés de Legendre <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 P_{\\\\ell }^{m}(x)}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msubsup>
<br/>          <mi>P</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>ℓ<!-- ℓ --></mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>m</mi>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle P_{\\\\ell }^{m}(x)}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a9b97f26a184f3993b6af4811375ec8b60e757b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.636ex; height:3.009ex;" alt="{\\\\displaystyle P_{\\\\ell }^{m}(x)}"></span>,  à des valeurs non-entières de <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 \\\\ell }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>ℓ<!-- ℓ --></mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\ell }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="\\\\ell "></span> et <span class="texhtml mvar" style="font-style:italic;">m</span>. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_de_Legendre">https://fr.wikipedia.org/wiki/Fonction_de_Legendre</a>)"""@fr, """In physical science and mathematics, the <b>Legendre functions</b> <span class="texhtml"><i>P</i><sub><i>λ</i></sub></span>, <span class="texhtml"><i>Q</i><sub><i>λ</i></sub></span> and <b>associated Legendre functions</b> <span class="texhtml"><i>P</i><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>μ</i></sup><br><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>λ</i></sub></span></span>, <span class="texhtml"><i>Q</i><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>μ</i></sup><br><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>λ</i></sub></span></span>, and <b>Legendre functions of the second kind</b>, <span class="texhtml"><i>Q<sub>n</sub></i></span>, are all solutions of Legendre's differential equation. The Legendre polynomials and the associated Legendre polynomials are also solutions of the differential equation in special cases, which, by virtue of being polynomials, have a large number of additional properties, mathematical structure, and applications. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Legendre_function">https://en.wikipedia.org/wiki/Legendre_function</a>)"""@en ;
  skos:prefLabel "Legendre function"@en, "fonction de Legendre"@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Legendre_function>, <https://fr.wikipedia.org/wiki/Fonction_de_Legendre> ;
  skos:broader psr:-FH1H1FB9-1 ;
  skos:inScheme psr: .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-QFN3LTHB-5 .