@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:-BLP2HLSP-6
  skos:prefLabel "calcul intégral"@fr, "integral calculus"@en ;
  a skos:Concept ;
  skos:narrower psr:-FV6T19JT-G .

psr:-VZ83B143-L
  skos:prefLabel "fonction hypergéométrique"@fr, "hypergeometric function"@en ;
  a skos:Concept ;
  skos:narrower psr:-FV6T19JT-G .

psr: a skos:ConceptScheme .
psr:-FV6T19JT-G
  skos:definition """En mathématiques, la fonction <b>exponentielle intégrale</b>, habituellement notée <span class="texhtml">Ei</span>, est définie par&nbsp;:
<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 {\\\\mbox{Ei}}:{\\egin{cases}\\\\mathbb {R} ^{*}\\	o \\\\mathbb {R} \\\\\\\\x\\\\mapsto {\\\\mbox{Ei}}(x)=-\\\\int _{-x}^{\\\\infty }{\\rac {{\\
m {e}}^{-t}}{t}}\\\\,\\\\mathrm {d} t\\\\,=\\\\int _{-\\\\infty }^{x}{\\rac {{\\
m {e}}^{t}}{t}}\\\\,\\\\mathrm {d} t.\\\\end{cases}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mstyle displaystyle="false" scriptlevel="0">
<br/>            <mtext>Ei</mtext>
<br/>          </mstyle>
<br/>        </mrow>
<br/>        <mo>:</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow>
<br/>            <mo>{</mo>
<br/>            <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false">
<br/>              <mtr>
<br/>                <mtd>
<br/>                  <msup>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mi mathvariant="double-struck">R</mi>
<br/>                    </mrow>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mo>∗<!-- ∗ --></mo>
<br/>                    </mrow>
<br/>                  </msup>
<br/>                  <mo stretchy="false">→<!-- → --></mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi mathvariant="double-struck">R</mi>
<br/>                  </mrow>
<br/>                </mtd>
<br/>              </mtr>
<br/>              <mtr>
<br/>                <mtd>
<br/>                  <mi>x</mi>
<br/>                  <mo stretchy="false">↦<!-- ↦ --></mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mstyle displaystyle="false" scriptlevel="0">
<br/>                      <mtext>Ei</mtext>
<br/>                    </mstyle>
<br/>                  </mrow>
<br/>                  <mo stretchy="false">(</mo>
<br/>                  <mi>x</mi>
<br/>                  <mo stretchy="false">)</mo>
<br/>                  <mo>=</mo>
<br/>                  <mo>−<!-- − --></mo>
<br/>                  <msubsup>
<br/>                    <mo>∫<!-- ∫ --></mo>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mo>−<!-- − --></mo>
<br/>                      <mi>x</mi>
<br/>                    </mrow>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>                    </mrow>
<br/>                  </msubsup>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mfrac>
<br/>                      <msup>
<br/>                        <mrow class="MJX-TeXAtom-ORD">
<br/>                          <mrow class="MJX-TeXAtom-ORD">
<br/>                            <mi mathvariant="normal">e</mi>
<br/>                          </mrow>
<br/>                        </mrow>
<br/>                        <mrow class="MJX-TeXAtom-ORD">
<br/>                          <mo>−<!-- − --></mo>
<br/>                          <mi>t</mi>
<br/>                        </mrow>
<br/>                      </msup>
<br/>                      <mi>t</mi>
<br/>                    </mfrac>
<br/>                  </mrow>
<br/>                  <mspace width="thinmathspace"></mspace>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi mathvariant="normal">d</mi>
<br/>                  </mrow>
<br/>                  <mi>t</mi>
<br/>                  <mspace width="thinmathspace"></mspace>
<br/>                  <mo>=</mo>
<br/>                  <msubsup>
<br/>                    <mo>∫<!-- ∫ --></mo>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mo>−<!-- − --></mo>
<br/>                      <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>                    </mrow>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mi>x</mi>
<br/>                    </mrow>
<br/>                  </msubsup>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mfrac>
<br/>                      <msup>
<br/>                        <mrow class="MJX-TeXAtom-ORD">
<br/>                          <mrow class="MJX-TeXAtom-ORD">
<br/>                            <mi mathvariant="normal">e</mi>
<br/>                          </mrow>
<br/>                        </mrow>
<br/>                        <mrow class="MJX-TeXAtom-ORD">
<br/>                          <mi>t</mi>
<br/>                        </mrow>
<br/>                      </msup>
<br/>                      <mi>t</mi>
<br/>                    </mfrac>
<br/>                  </mrow>
<br/>                  <mspace width="thinmathspace"></mspace>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi mathvariant="normal">d</mi>
<br/>                  </mrow>
<br/>                  <mi>t</mi>
<br/>                  <mo>.</mo>
<br/>                </mtd>
<br/>              </mtr>
<br/>            </mtable>
<br/>            <mo fence="true" stretchy="true" symmetric="true"></mo>
<br/>          </mrow>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\\\mbox{Ei}}:{\\egin{cases}\\\\mathbb {R} ^{*}\\	o \\\\mathbb {R} \\\\\\\\x\\\\mapsto {\\\\mbox{Ei}}(x)=-\\\\int _{-x}^{\\\\infty }{\\rac {{\\
m {e}}^{-t}}{t}}\\\\,\\\\mathrm {d} t\\\\,=\\\\int _{-\\\\infty }^{x}{\\rac {{\\
m {e}}^{t}}{t}}\\\\,\\\\mathrm {d} t.\\\\end{cases}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4150bba3e42bca947e2681d52ac99bd3c75425b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.838ex; width:45.475ex; height:6.843ex;" alt="{\\\\displaystyle {\\\\mbox{Ei}}:{\\egin{cases}\\\\mathbb {R} ^{*}\\	o \\\\mathbb {R} \\\\\\\\x\\\\mapsto {\\\\mbox{Ei}}(x)=-\\\\int _{-x}^{\\\\infty }{\\rac {{\\
m {e}}^{-t}}{t}}\\\\,\\\\mathrm {d} t\\\\,=\\\\int _{-\\\\infty }^{x}{\\rac {{\\
m {e}}^{t}}{t}}\\\\,\\\\mathrm {d} t.\\\\end{cases}}}"></span></dd></dl>
<br/>Comme l'intégrale de la fonction inverse (<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 t\\\\mapsto {\\rac {1}{t}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>t</mi>
<br/>        <mo stretchy="false">↦<!-- ↦ --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mi>t</mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle t\\\\mapsto {\\rac {1}{t}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0af9f10c0816c62a85b7e3177a73cc3518d8b036" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:6.452ex; height:5.176ex;" alt="{\\\\displaystyle t\\\\mapsto {\\rac {1}{t}}}"></span>) diverge en 0, cette définition doit être comprise, si <span class="texhtml"><i>x</i> &gt; 0</span>, comme une valeur principale de Cauchy. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Exponentielle_int%C3%A9grale">https://fr.wikipedia.org/wiki/Exponentielle_int%C3%A9grale</a>)"""@fr, """In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Exponential_integral">https://en.wikipedia.org/wiki/Exponential_integral</a>)"""@en ;
  skos:narrower psr:-TBZZXZMC-3 ;
  skos:prefLabel "exponential integral"@en, "exponentielle intégrale"@fr ;
  a skos:Concept ;
  skos:broader psr:-VZ83B143-L, psr:-BLP2HLSP-6 ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Exponential_integral>, <https://fr.wikipedia.org/wiki/Exponentielle_int%C3%A9grale> ;
  dc:modified "2023-08-17"^^xsd:date ;
  dc:created "2023-07-27"^^xsd:date .

psr:-TBZZXZMC-3
  skos:prefLabel "Bickley-Naylor function"@en, "fonction de Bickley-Naylor"@fr ;
  a skos:Concept ;
  skos:broader psr:-FV6T19JT-G .