@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:-L62WCRCG-J
  skos:prefLabel "inégalité de Lebedev-Milin"@fr, "Lebedev-Milin inequality"@en ;
  a skos:Concept ;
  skos:related psr:-CDSQH02T-4 .

psr:-CDSQH02T-4
  skos:broader psr:-MHPG0QZH-R, psr:-B3GGSQMX-3, psr:-RN57KZJ9-9 ;
  skos:definition """In mathematics, a <b>power series</b> (in one variable) is an infinite series of the form
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\sum _{n=0}^{\\\\infty }a_{n}\\\\left(x-c\\
ight)^{n}=a_{0}+a_{1}(x-c)+a_{2}(x-c)^{2}+\\\\dots }">
<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>0</mn>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </munderover>
<br/>        <msub>
<br/>          <mi>a</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msup>
<br/>          <mrow>
<br/>            <mo>(</mo>
<br/>            <mrow>
<br/>              <mi>x</mi>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mi>c</mi>
<br/>            </mrow>
<br/>            <mo>)</mo>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>=</mo>
<br/>        <msub>
<br/>          <mi>a</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>a</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mi>c</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>+</mo>
<br/>        <msub>
<br/>          <mi>a</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mi>c</mi>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mo>…<!-- … --></mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sum _{n=0}^{\\\\infty }a_{n}\\\\left(x-c\\
ight)^{n}=a_{0}+a_{1}(x-c)+a_{2}(x-c)^{2}+\\\\dots }</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd004cd5d1b1c964aaf976ed5c13587c6829c845" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -3.005ex; width:50.617ex; height:6.843ex;" alt="{\\\\displaystyle \\\\sum _{n=0}^{\\\\infty }a_{n}\\\\left(x-c\\
ight)^{n}=a_{0}+a_{1}(x-c)+a_{2}(x-c)^{2}+\\\\dots }"></div>
<br/>where <i>a<sub>n</sub></i> represents the coefficient of the <i>n</i>th term and <i>c</i> is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Power_series">https://en.wikipedia.org/wiki/Power_series</a>)"""@en, """En mathématiques et particulièrement en analyse, une <b>série entière</b> est une série de fonctions de la forme
<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 \\\\sum a_{n}z^{n}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mo>∑<!-- ∑ --></mo>
<br/>        <msub>
<br/>          <mi>a</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <msup>
<br/>          <mi>z</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sum a_{n}z^{n}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3e79a3a10552c880890a247484ae3c55ba076e9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.338ex; width:8.499ex; height:3.843ex;" alt="{\\\\displaystyle \\\\sum a_{n}z^{n}}"></span></dd></dl>
<br/>où les coefficients <span class="texhtml mvar" style="font-style:italic;">a<sub>n</sub></span> forment une suite réelle ou complexe. Une explication de ce terme est qu'au XVII<sup style="font-size:72%">e</sup> siècle, on appelle fonctions entières des fonctions définies sur tout le plan complexe. On parle de séries entières lorsqu'elles s'expriment sous forme de séries en <span class="texhtml mvar" style="font-style:italic;">a<sub>n</sub>x<sup>n</sup></span>. Par extension, ce nom s'est généralisé pour les séries entières de rayon de convergence fini&nbsp;»</span>. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/S%C3%A9rie_enti%C3%A8re">https://fr.wikipedia.org/wiki/S%C3%A9rie_enti%C3%A8re</a>)"""@fr ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:related psr:-L62WCRCG-J, psr:-D7VZQ60F-N ;
  skos:prefLabel "série entière"@fr, "power series"@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/S%C3%A9rie_enti%C3%A8re>, <https://en.wikipedia.org/wiki/Power_series> ;
  dc:modified "2023-08-03"^^xsd:date .

psr:-D7VZQ60F-N
  skos:prefLabel "série génératrice"@fr, "generating function"@en ;
  a skos:Concept ;
  skos:related psr:-CDSQH02T-4 .

psr: a skos:ConceptScheme .
psr:-B3GGSQMX-3
  skos:prefLabel "série"@fr, "series"@en ;
  a skos:Concept ;
  skos:narrower psr:-CDSQH02T-4 .

psr:-MHPG0QZH-R
  skos:prefLabel "multivariable calculus"@en, "calcul multivariable"@fr ;
  a skos:Concept ;
  skos:narrower psr:-CDSQH02T-4 .

psr:-RN57KZJ9-9
  skos:prefLabel "analyse complexe"@fr, "complex analysis"@en ;
  a skos:Concept ;
  skos:narrower psr:-CDSQH02T-4 .