@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:-P93ST75Z-8
  skos:prefLabel "théorie des nombres"@fr, "number theory"@en ;
  a skos:Concept ;
  skos:narrower psr:-QTJR2P0K-4 .

psr: a skos:ConceptScheme .
psr:-QTJR2P0K-4
  dc:modified "2023-08-24"^^xsd:date ;
  skos:definition """En mathématiques, la constante de Meissel-Mertens (également nommée constante de Mertens, constante de Kronecker, constante de Hadamard-La Vallée Poussin ou constante des inverses des nombres premiers) est utilisée principalement en théorie des nombres. Elle est définie comme la limite de la différence entre la série des inverses des nombres premiers et le logarithme népérien du logarithme népérien. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Constante_de_Meissel-Mertens">https://fr.wikipedia.org/wiki/Constante_de_Meissel-Mertens</a>)"""@fr, """The <b>Meissel–Mertens constant</b> (named after Ernst Meissel and Franz Mertens), also referred to as <b>Mertens constant</b>, <b>Kronecker's constant</b>, <b>Hadamard–de la Vallée-Poussin constant</b> or the <b>prime reciprocal constant</b>, is a mathematical constant in number theory, defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm:
<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 M=\\\\lim _{n\\
ightarrow \\\\infty }\\\\left(\\\\sum _{p\\\\leq n}{\\rac {1}{p}}-\\\\ln(\\\\ln n)\\
ight)=\\\\gamma +\\\\sum _{p}\\\\left[\\\\ln \\\\!\\\\left(1-{\\rac {1}{p}}\\
ight)+{\\rac {1}{p}}\\
ight].}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>M</mi>
<br/>        <mo>=</mo>
<br/>        <munder>
<br/>          <mo movablelimits="true" form="prefix">lim</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo stretchy="false">→<!-- → --></mo>
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </munder>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <munder>
<br/>              <mo>∑<!-- ∑ --></mo>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>p</mi>
<br/>                <mo>≤<!-- ≤ --></mo>
<br/>                <mi>n</mi>
<br/>              </mrow>
<br/>            </munder>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mn>1</mn>
<br/>                <mi>p</mi>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>ln</mi>
<br/>            <mo>⁡<!-- ⁡ --></mo>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>ln</mi>
<br/>            <mo>⁡<!-- ⁡ --></mo>
<br/>            <mi>n</mi>
<br/>            <mo stretchy="false">)</mo>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mi>γ<!-- γ --></mi>
<br/>        <mo>+</mo>
<br/>        <munder>
<br/>          <mo>∑<!-- ∑ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>p</mi>
<br/>          </mrow>
<br/>        </munder>
<br/>        <mrow>
<br/>          <mo>[</mo>
<br/>          <mrow>
<br/>            <mi>ln</mi>
<br/>            <mspace width="negativethinmathspace"></mspace>
<br/>            <mrow>
<br/>              <mo>(</mo>
<br/>              <mrow>
<br/>                <mn>1</mn>
<br/>                <mo>−<!-- − --></mo>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mfrac>
<br/>                    <mn>1</mn>
<br/>                    <mi>p</mi>
<br/>                  </mfrac>
<br/>                </mrow>
<br/>              </mrow>
<br/>              <mo>)</mo>
<br/>            </mrow>
<br/>            <mo>+</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mn>1</mn>
<br/>                <mi>p</mi>
<br/>              </mfrac>
<br/>            </mrow>
<br/>          </mrow>
<br/>          <mo>]</mo>
<br/>        </mrow>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle M=\\\\lim _{n\\
ightarrow \\\\infty }\\\\left(\\\\sum _{p\\\\leq n}{\\rac {1}{p}}-\\\\ln(\\\\ln n)\\
ight)=\\\\gamma +\\\\sum _{p}\\\\left[\\\\ln \\\\!\\\\left(1-{\\rac {1}{p}}\\
ight)+{\\rac {1}{p}}\\
ight].}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0284c04584369156c34bad21ea0010f128f8696" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.338ex; width:60.587ex; height:7.676ex;" alt="{\\\\displaystyle M=\\\\lim _{n\\
ightarrow \\\\infty }\\\\left(\\\\sum _{p\\\\leq n}{\\rac {1}{p}}-\\\\ln(\\\\ln n)\\
ight)=\\\\gamma +\\\\sum _{p}\\\\left[\\\\ln \\\\!\\\\left(1-{\\rac {1}{p}}\\
ight)+{\\rac {1}{p}}\\
ight].}"></span></dd></dl>
<br/>Here γ is the Euler–Mascheroni constant, which has an analogous definition involving a sum over all integers (not just the primes).
<br/> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constant">https://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constant</a>)"""@en ;
  skos:altLabel "prime reciprocal constant"@en, "Hadamard-de la Vallée-Poussin constant"@en, "constante des inverses des nombres premiers"@fr, "constante de Hadamard-La Vallée Poussin"@fr, "Kronecker's constant"@en, "Mertens constant"@en, "constante de Mertens"@fr, "constante de Kronecker"@fr ;
  skos:prefLabel "constante de Meissel-Mertens"@fr, "Meissel-Mertens constant"@en ;
  dc:created "2023-08-03"^^xsd:date ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constant>, <https://fr.wikipedia.org/wiki/Constante_de_Meissel-Mertens> ;
  skos:inScheme psr: ;
  skos:broader psr:-P93ST75Z-8, psr:-RBFVN7DN-2 ;
  a skos:Concept .

psr:-RBFVN7DN-2
  skos:prefLabel "mathematical constant"@en, "constante mathématique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-QTJR2P0K-4 .