@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:-SNTKWPJM-D
  skos:prefLabel "polynôme"@fr, "polynomial"@en ;
  a skos:Concept ;
  skos:narrower psr:-MH5LQFJL-B .

psr:-MH5LQFJL-B
  skos:definition """The <b>Abel polynomials</b> are a sequence of polynomials named after Niels Henrik Abel, defined by the following equation:
<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 p_{n}(x)=x(x-an)^{n-1}}">
<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>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mi>a</mi>
<br/>        <mi>n</mi>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle p_{n}(x)=x(x-an)^{n-1}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/207ea215895fee8446ab13b487d8418da714d00f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:21.967ex; height:3.176ex;" alt="{\\\\displaystyle p_{n}(x)=x(x-an)^{n-1}}"></span></dd></dl>
<br/>This polynomial sequence is of binomial type: conversely, every polynomial sequence of binomial type may be obtained from the Abel sequence using umbral calculus. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Abel_polynomials">https://en.wikipedia.org/wiki/Abel_polynomials</a>)"""@en, """En mathématiques, les <b>polynômes d'Abel</b> forment une suite de polynômes dont le <span class="texhtml"><i>n</i></span>-ième est de la forme
<br/>
<br/><div class="center"><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 A_{n}(x)=x(x-an)^{n-1}.~}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>A</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mi>a</mi>
<br/>        <mi>n</mi>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>.</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle A_{n}(x)=x(x-an)^{n-1}.~}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d0a2e35f3bc8422862f818a178d186dabddbc8b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.066ex; height:3.176ex;" alt="{\\\\displaystyle A_{n}(x)=x(x-an)^{n-1}.~}"></span></div>
<br/>Cette suite de polynômes est de type binomial. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Polyn%C3%B4me_d%27Abel">https://fr.wikipedia.org/wiki/Polyn%C3%B4me_d%27Abel</a>)"""@fr ;
  skos:prefLabel "Abel polynomial"@en, "polynôme d'Abel"@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Abel_polynomials>, <https://fr.wikipedia.org/wiki/Polyn%C3%B4me_d%27Abel> ;
  skos:broader psr:-FH1H1FB9-1, psr:-SNTKWPJM-D ;
  skos:inScheme psr: ;
  a skos:Concept ;
  dc:created "2023-08-16"^^xsd:date ;
  dc:modified "2023-08-16"^^xsd:date .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-MH5LQFJL-B .