@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr: a skos:ConceptScheme .
psr:-HT1VBDWN-F
  skos:definition """La fonction sinus hyperbolique, notée <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 \\\\sinh }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>sinh</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sinh }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb6649e190c30e91b280cc02b27acdfe00055e58" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.148ex; height:2.176ex;" alt="\\\\sinh"></span> (ou <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 \\\\operatorname {sh} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>sh</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\operatorname {sh} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e006cd182ab99b080ffc693f7c02b1b0f96e8a4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.209ex; height:2.176ex;" alt="{\\\\displaystyle \\\\operatorname {sh} }"></span>) est la fonction complexe suivante&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 \\\\sinh :z\\\\mapsto {\\rac {\\\\mathrm {e} ^{z}-\\\\mathrm {e} ^{-z}}{2}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>sinh</mi>
<br/>        <mo>:</mo>
<br/>        <mi>z</mi>
<br/>        <mo stretchy="false">↦<!-- ↦ --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <msup>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi mathvariant="normal">e</mi>
<br/>                </mrow>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi>z</mi>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mo>−<!-- − --></mo>
<br/>              <msup>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi mathvariant="normal">e</mi>
<br/>                </mrow>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mo>−<!-- − --></mo>
<br/>                  <mi>z</mi>
<br/>                </mrow>
<br/>              </msup>
<br/>            </mrow>
<br/>            <mn>2</mn>
<br/>          </mfrac>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sinh :z\\\\mapsto {\\rac {\\\\mathrm {e} ^{z}-\\\\mathrm {e} ^{-z}}{2}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af00de933d5f59574ccfa70de14d079eccaed387" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:19.811ex; height:5.509ex;" alt="{\\\\displaystyle \\\\sinh :z\\\\mapsto {\\rac {\\\\mathrm {e} ^{z}-\\\\mathrm {e} ^{-z}}{2}}}"></span></dd></dl>
<br/>où <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 z\\\\mapsto \\\\mathrm {e} ^{z}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>z</mi>
<br/>        <mo stretchy="false">↦<!-- ↦ --></mo>
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">e</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>z</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle z\\\\mapsto \\\\mathrm {e} ^{z}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b509eafc077fafb60447d21114e80d0266793b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:6.736ex; height:2.343ex;" alt="{\\\\displaystyle z\\\\mapsto \\\\mathrm {e} ^{z}}"></span> est l'exponentielle complexe.
<br/>La fonction sinus hyperbolique est la partie impaire de l'exponentielle complexe.
<br/>Dans la géométrie hyperbolique, la fonction sinus hyperbolique est un analogue de la fonction sinus de la géométrie euclidienne. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Sinus_hyperbolique">https://fr.wikipedia.org/wiki/Sinus_hyperbolique</a>)"""@fr ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-R92BT00M-4 ;
  skos:prefLabel "hyperbolic sine"@en, "sinus hyperbolique"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Sinus_hyperbolique> .

psr:-R92BT00M-4
  skos:prefLabel "hyperbolic function"@en, "fonction hyperbolique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-HT1VBDWN-F .