@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:-RBFVN7DN-2
  skos:prefLabel "mathematical constant"@en, "constante mathématique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-GMDCHPH4-N .

psr:-BBJ50HB6-6
  skos:prefLabel "Apéry's theorem"@en, "théorème d'Apéry"@fr ;
  a skos:Concept ;
  skos:related psr:-GMDCHPH4-N .

psr: a skos:ConceptScheme .
psr:-P36V4MHV-V
  skos:prefLabel "fonction zêta de Riemann"@fr, "Riemann zeta function"@en ;
  a skos:Concept ;
  skos:narrower psr:-GMDCHPH4-N .

psr:-GMDCHPH4-N
  a skos:Concept ;
  skos:broader psr:-P36V4MHV-V, psr:-RBFVN7DN-2 ;
  dc:created "2023-08-03"^^xsd:date ;
  skos:definition """En analyse mathématique, la <b>constante d'Apéry</b> est la valeur en <span class="texhtml">3</span> de la fonction zêta de Riemann :  <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 \\\\zeta (3)=\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{3}}}\\\\approx 1{,}202}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>ζ<!-- ζ --></mi>         <mo stretchy="false">(</mo>         <mn>3</mn>         <mo stretchy="false">)</mo>         <mo>=</mo>         <munderover>           <mo>∑<!-- ∑ --></mo>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>             <mo>=</mo>             <mn>1</mn>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mi mathvariant="normal">∞<!-- ∞ --></mi>           </mrow>         </munderover>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <msup>               <mi>n</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mn>3</mn>               </mrow>             </msup>           </mfrac>         </mrow>         <mo>≈<!-- ≈ --></mo>         <mn>1,202</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\zeta (3)=\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{3}}}\\\\approx 1{,}202}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3854181f1e471229355ba826b2da27f073a0ee2a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:22.588ex; height:6.843ex;" alt="{\\\\displaystyle \\\\zeta (3)=\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{3}}}\\\\approx 1{,}202}"></span></span>.</center> Elle porte le nom de Roger Apéry, qui a montré en 1978 que ce nombre est irrationnel. On n'en connaît pas de forme fermée. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Constante_d%27Ap%C3%A9ry">https://fr.wikipedia.org/wiki/Constante_d%27Ap%C3%A9ry</a>)"""@fr, """In mathematics, <b>Apéry's constant</b> is the sum of the reciprocals of the positive cubes. That is, it is defined as the number  <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 {\\egin{aligned}\\\\zeta (3)&amp;=\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{3}}}\\\\\\\\&amp;=\\\\lim _{n\\	o \\\\infty }\\\\left({\\rac {1}{1^{3}}}+{\\rac {1}{2^{3}}}+\\\\cdots +{\\rac {1}{n^{3}}}\\
ight),\\\\end{aligned}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">             <mtr>               <mtd>                 <mi>ζ<!-- ζ --></mi>                 <mo stretchy="false">(</mo>                 <mn>3</mn>                 <mo stretchy="false">)</mo>               </mtd>               <mtd>                 <mi></mi>                 <mo>=</mo>                 <munderover>                   <mo>∑<!-- ∑ --></mo>                   <mrow class="MJX-TeXAtom-ORD">                     <mi>n</mi>                     <mo>=</mo>                     <mn>1</mn>                   </mrow>                   <mrow class="MJX-TeXAtom-ORD">                     <mi mathvariant="normal">∞<!-- ∞ --></mi>                   </mrow>                 </munderover>                 <mrow class="MJX-TeXAtom-ORD">                   <mfrac>                     <mn>1</mn>                     <msup>                       <mi>n</mi>                       <mrow class="MJX-TeXAtom-ORD">                         <mn>3</mn>                       </mrow>                     </msup>                   </mfrac>                 </mrow>               </mtd>             </mtr>             <mtr>               <mtd></mtd>               <mtd>                 <mi></mi>                 <mo>=</mo>                 <munder>                   <mo movablelimits="true" form="prefix">lim</mo>                   <mrow class="MJX-TeXAtom-ORD">                     <mi>n</mi>                     <mo stretchy="false">→<!-- → --></mo>                     <mi mathvariant="normal">∞<!-- ∞ --></mi>                   </mrow>                 </munder>                 <mrow>                   <mo>(</mo>                   <mrow>                     <mrow class="MJX-TeXAtom-ORD">                       <mfrac>                         <mn>1</mn>                         <msup>                           <mn>1</mn>                           <mrow class="MJX-TeXAtom-ORD">                             <mn>3</mn>                           </mrow>                         </msup>                       </mfrac>                     </mrow>                     <mo>+</mo>                     <mrow class="MJX-TeXAtom-ORD">                       <mfrac>                         <mn>1</mn>                         <msup>                           <mn>2</mn>                           <mrow class="MJX-TeXAtom-ORD">                             <mn>3</mn>                           </mrow>                         </msup>                       </mfrac>                     </mrow>                     <mo>+</mo>                     <mo>⋯<!-- ⋯ --></mo>                     <mo>+</mo>                     <mrow class="MJX-TeXAtom-ORD">                       <mfrac>                         <mn>1</mn>                         <msup>                           <mi>n</mi>                           <mrow class="MJX-TeXAtom-ORD">                             <mn>3</mn>                           </mrow>                         </msup>                       </mfrac>                     </mrow>                   </mrow>                   <mo>)</mo>                 </mrow>                 <mo>,</mo>               </mtd>             </mtr>           </mtable>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\egin{aligned}\\\\zeta (3)&amp;=\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{3}}}\\\\\\\\&amp;=\\\\lim _{n\\	o \\\\infty }\\\\left({\\rac {1}{1^{3}}}+{\\rac {1}{2^{3}}}+\\\\cdots +{\\rac {1}{n^{3}}}\\
ight),\\\\end{aligned}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9740534aa2a7c7a2158052e4a0edc48e5276655f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:37.667ex; height:13.176ex;" alt="{\\\\displaystyle {\\egin{aligned}\\\\zeta (3)&amp;=\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{3}}}\\\\\\\\&amp;=\\\\lim _{n\\	o \\\\infty }\\\\left({\\rac {1}{1^{3}}}+{\\rac {1}{2^{3}}}+\\\\cdots +{\\rac {1}{n^{3}}}\\
ight),\\\\end{aligned}}}"></span></dd></dl> where <span class="texhtml mvar" style="font-style:italic;">ζ</span> is the Riemann zeta function. It has an approximate value of  <dl><dd><span class="texhtml"><i>ζ</i>(3) = <span style="white-space:nowrap">1.20205<span style="margin-left:0.25em">69031</span><span style="margin-left:0.25em">59594</span><span style="margin-left:0.25em">28539</span><span style="margin-left:0.25em">97381</span><span style="margin-left:0.25em">61511</span><span style="margin-left:0.25em">44999</span><span style="margin-left:0.25em">07649</span><span style="margin-left:0.25em">86292</span><span style="margin-left:0.25em">…</span></span></span> (sequence A002117 in the OEIS).</dd></dl> The constant is named after Roger Apéry. It arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio using quantum electrodynamics. It also arises in the analysis of random minimum spanning trees and in conjunction with the gamma function when solving certain integrals involving exponential functions in a quotient, which appear occasionally in physics, for instance, when evaluating the two-dimensional case of the Debye model and the Stefan–Boltzmann law. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant">https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant</a>)"""@en ;
  skos:prefLabel "Apéry's constant"@en, "constante d'Apéry"@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant>, <https://fr.wikipedia.org/wiki/Constante_d%27Ap%C3%A9ry> ;
  skos:related psr:-BBJ50HB6-6 ;
  skos:inScheme psr: ;
  dc:modified "2024-10-18"^^xsd:date .