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

psr: a skos:ConceptScheme .
psr:-L73X73X9-S
  skos:definition """La fonction cosinus 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 \\\\cosh }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>cosh</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\cosh }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/011ccafd311d38f9bbc0fcf3f7b13f7d81469d84" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.404ex; height:2.176ex;" alt="\\\\cosh"></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 {ch} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>ch</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\operatorname {ch} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09dc7ce210c0c1e878674928a3445ed845617bd1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.325ex; height:2.176ex;" alt="{\\\\displaystyle \\\\operatorname {ch} }"></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 {\\egin{matrix}\\\\cosh :&amp;\\\\mathbb {C} &amp;\\	o &amp;\\\\mathbb {C} \\\\\\\\&amp;z&amp;\\\\mapsto &amp;\\\\displaystyle {\\rac {\\\\operatorname {e} ^{z}+\\\\operatorname {e} ^{-z}}{2}}\\\\end{matrix}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtable rowspacing="4pt" columnspacing="1em">
<br/>            <mtr>
<br/>              <mtd>
<br/>                <mi>cosh</mi>
<br/>                <mo>:</mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi mathvariant="double-struck">C</mi>
<br/>                </mrow>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mo stretchy="false">→<!-- → --></mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi mathvariant="double-struck">C</mi>
<br/>                </mrow>
<br/>              </mtd>
<br/>            </mtr>
<br/>            <mtr>
<br/>              <mtd></mtd>
<br/>              <mtd>
<br/>                <mi>z</mi>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mo stretchy="false">↦<!-- ↦ --></mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mstyle displaystyle="true" scriptlevel="0">
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mfrac>
<br/>                      <mrow>
<br/>                        <msup>
<br/>                          <mi mathvariant="normal">e</mi>
<br/>                          <mrow class="MJX-TeXAtom-ORD">
<br/>                            <mi>z</mi>
<br/>                          </mrow>
<br/>                        </msup>
<br/>                        <mo>+</mo>
<br/>                        <msup>
<br/>                          <mi mathvariant="normal">e</mi>
<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/>              </mtd>
<br/>            </mtr>
<br/>          </mtable>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\egin{matrix}\\\\cosh :&amp;\\\\mathbb {C} &amp;\\	o &amp;\\\\mathbb {C} \\\\\\\\&amp;z&amp;\\\\mapsto &amp;\\\\displaystyle {\\rac {\\\\operatorname {e} ^{z}+\\\\operatorname {e} ^{-z}}{2}}\\\\end{matrix}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79cc239fd15cce3caf208f520010d64ac77c3033" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.838ex; width:26.182ex; height:8.843ex;" alt="{\\\\displaystyle {\\egin{matrix}\\\\cosh :&amp;\\\\mathbb {C} &amp;\\	o &amp;\\\\mathbb {C} \\\\\\\\&amp;z&amp;\\\\mapsto &amp;\\\\displaystyle {\\rac {\\\\operatorname {e} ^{z}+\\\\operatorname {e} ^{-z}}{2}}\\\\end{matrix}}}"></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 \\\\operatorname {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/>          <mi mathvariant="normal">e</mi>
<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 \\\\operatorname {e} ^{z}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3de830b5be106d1ff2f26f37d1647c87f76c953" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:6.736ex; height:2.343ex;" alt="{\\\\displaystyle z\\\\mapsto \\\\operatorname {e} ^{z}}"></span> est l'exponentielle complexe.
<br/>La fonction cosinus hyperbolique est donc la partie paire de l'exponentielle complexe. Elle se restreint en une fonction réelle d'une variable réelle. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Cosinus_hyperbolique">https://fr.wikipedia.org/wiki/Cosinus_hyperbolique</a>)"""@fr ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-R92BT00M-4 ;
  skos:prefLabel "cosinus hyperbolique"@fr, "hyperbolic cosine"@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Cosinus_hyperbolique> .

psr:-R92BT00M-4
  skos:prefLabel "hyperbolic function"@en, "fonction hyperbolique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-L73X73X9-S .