@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:-T36RJ8T9-6
  skos:prefLabel "Hurwitz zeta function"@en, "fonction zêta de Hurwitz"@fr ;
  a skos:Concept ;
  skos:related psr:-NHDPQMVR-B .

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

psr:-NHDPQMVR-B
  skos:broader psr:-NHFK3Q1R-H, psr:-B3GGSQMX-3, psr:-XZBJ865P-9 ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/S%C3%A9rie_z%C3%AAta_rationnelle>, <https://en.wikipedia.org/wiki/Rational_zeta_series> ;
  dc:modified "2023-08-04"^^xsd:date ;
  skos:related psr:-P36V4MHV-V, psr:-T36RJ8T9-6 ;
  a skos:Concept ;
  skos:definition """In mathematics, a <b>rational zeta series</b> is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function.  Specifically, given a real number <i>x</i>, the rational zeta series for <i>x</i> is given by
<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 x=\\\\sum _{n=2}^{\\\\infty }q_{n}\\\\zeta (n,m)}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>x</mi>
<br/>        <mo>=</mo>
<br/>        <munderover>
<br/>          <mo>∑<!-- ∑ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>=</mo>
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </munderover>
<br/>        <msub>
<br/>          <mi>q</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mi>ζ<!-- ζ --></mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>n</mi>
<br/>        <mo>,</mo>
<br/>        <mi>m</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle x=\\\\sum _{n=2}^{\\\\infty }q_{n}\\\\zeta (n,m)}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d401704a10ea6c5053b45a41a797051e17169bc2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:17.799ex; height:6.843ex;" alt="{\\\\displaystyle x=\\\\sum_{n=2}^\\\\infty q_n \\\\zeta (n,m)}"></span></dd></dl>
<br/>where <i>q</i><sub><i>n</i></sub> is a rational number, the value <i>m</i> is held fixed, and ζ(<i>s</i>,&nbsp;<i>m</i>) is the Hurwitz zeta function.  It is not hard to show that any real number <i>x</i> can be expanded in this way.
<br/> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Rational_zeta_series">https://en.wikipedia.org/wiki/Rational_zeta_series</a>)"""@en, """En mathématiques, une série zêta rationnelle est la représentation d'un nombre réel arbitraire en termes d'une série constituée de nombres rationnels et de la fonction zêta de Riemann ou de la fonction zêta de Hurwitz. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/S%C3%A9rie_z%C3%AAta_rationnelle">https://fr.wikipedia.org/wiki/S%C3%A9rie_z%C3%AAta_rationnelle</a>)"""@fr ;
  skos:prefLabel "série zêta rationnelle"@fr, "rational zeta series"@en ;
  dc:created "2023-08-04"^^xsd:date ;
  skos:inScheme psr: .

psr:-XZBJ865P-9
  skos:prefLabel "nombre réel"@fr, "real number"@en ;
  a skos:Concept ;
  skos:narrower psr:-NHDPQMVR-B .

psr: a skos:ConceptScheme .
psr:-B3GGSQMX-3
  skos:prefLabel "série"@fr, "series"@en ;
  a skos:Concept ;
  skos:narrower psr:-NHDPQMVR-B .

psr:-P36V4MHV-V
  skos:prefLabel "fonction zêta de Riemann"@fr, "Riemann zeta function"@en ;
  a skos:Concept ;
  skos:related psr:-NHDPQMVR-B .