@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:-NHFK3Q1R-H
  skos:prefLabel "fonction L"@fr, "L-function"@en ;
  a skos:Concept ;
  skos:narrower psr:-NB4Q73Q0-K .

psr:-LFK6NSF9-J
  skos:prefLabel "analyse harmonique"@fr, "harmonic analysis"@en ;
  a skos:Concept ;
  skos:narrower psr:-NB4Q73Q0-K .

psr: a skos:ConceptScheme .
psr:-NB4Q73Q0-K
  skos:broader psr:-LFK6NSF9-J, psr:-B3GGSQMX-3, psr:-NHFK3Q1R-H ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Basel_problem>, <https://fr.wikipedia.org/wiki/Probl%C3%A8me_de_B%C3%A2le> ;
  skos:prefLabel "Basel problem"@en, "problème de Bâle"@fr ;
  skos:definition """En mathématiques, le <b>problème de Bâle</b> (connu parfois aussi sous le nom de <b>problème de Mengoli</b>) est un problème renommé de théorie des nombres, qui consiste à demander la valeur de la somme de la série convergente&nbsp;:
<br/>
<br/><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 {\\rac {1}{1^{2}}}+{\\rac {1}{2^{2}}}+{\\rac {1}{3^{2}}}+{\\rac {1}{4^{2}}}+\\\\cdots }">
<br/>  <semantics>
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<br/>            <mn>1</mn>
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<br/>                <mn>2</mn>
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<br/>        <mo>⋯<!-- ⋯ --></mo>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {1}{1^{2}}}+{\\rac {1}{2^{2}}}+{\\rac {1}{3^{2}}}+{\\rac {1}{4^{2}}}+\\\\cdots }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18bd3e16f388e1a3dfb61be7efadde286f78ff8f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.296ex; height:5.676ex;" alt="{\\\\displaystyle {\\rac {1}{1^{2}}}+{\\rac {1}{2^{2}}}+{\\rac {1}{3^{2}}}+{\\rac {1}{4^{2}}}+\\\\cdots }"></span></center>
<br/>Le problème a été résolu par Leonhard Euler, qui établit que cette somme <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 \\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{2}}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <munderover>
<br/>          <mo>∑<!-- ∑ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>=</mo>
<br/>            <mn>1</mn>
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<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
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<br/>          <mfrac>
<br/>            <mn>1</mn>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{2}}}}</annotation>
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<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b42204c71e0c7128ff6f317abcb1deea9c6a946" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:7.027ex; height:6.843ex;" alt="{\\\\displaystyle \\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n^{2}}}}"></span> vaut&nbsp;:
<br/>
<br/><dl><dd><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 {\\rac {\\\\pi ^{2}}{6}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
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<br/>          <mfrac>
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<br/>              <mi>π<!-- π --></mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
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<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {\\\\pi ^{2}}{6}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e0450af1a6ef356bc0061f8089319332fdde755" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.225ex; height:5.676ex;" alt="{\\\\displaystyle {\\rac {\\\\pi ^{2}}{6}}}"></span></center></dd></dl>
<br/>et en donna une première preuve en 1735, puis une deuxième, plus rigoureuse, en 1741. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Probl%C3%A8me_de_B%C3%A2le">https://fr.wikipedia.org/wiki/Probl%C3%A8me_de_B%C3%A2le</a>)"""@fr, """The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up more than a century later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties. The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Basel_problem">https://en.wikipedia.org/wiki/Basel_problem</a>)"""@en ;
  skos:related psr:-LRPB5V08-Q ;
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  skos:inScheme psr: ;
  dc:created "2023-08-18"^^xsd:date ;
  dc:modified "2023-08-28"^^xsd:date .

psr:-B3GGSQMX-3
  skos:prefLabel "série"@fr, "series"@en ;
  a skos:Concept ;
  skos:narrower psr:-NB4Q73Q0-K .

psr:-LRPB5V08-Q
  skos:prefLabel "square number"@en, "nombre carré"@fr ;
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  skos:related psr:-NB4Q73Q0-K .