@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: a skos:ConceptScheme .
psr:-RT4H0VFD-8
  a skos:Concept ;
  skos:broader psr:-FM1M1PDT-5, psr:-BSS33T4W-C ;
  skos:prefLabel "factorielle exponentielle"@fr, "exponential factorial"@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Factorielle_exponentielle>, <https://en.wikipedia.org/wiki/Exponential_factorial> ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """Une <b>factorielle exponentielle</b> est un entier naturel <i>n</i> élevé à la puissance <span class="nowrap"><i>n</i> – 1</span>, qui à son tour est élevé à la puissance <span class="nowrap"><i>n</i> – 2</span>, et ainsi de suite, c.-à-d. :  <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 n^{(n-1)^{(n-2)\\\\cdots }}.}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>n</mi>           <mrow class="MJX-TeXAtom-ORD">             <mo stretchy="false">(</mo>             <mi>n</mi>             <mo>−<!-- − --></mo>             <mn>1</mn>             <msup>               <mo stretchy="false">)</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mo stretchy="false">(</mo>                 <mi>n</mi>                 <mo>−<!-- − --></mo>                 <mn>2</mn>                 <mo stretchy="false">)</mo>                 <mo>⋯<!-- ⋯ --></mo>               </mrow>             </msup>           </mrow>         </msup>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle n^{(n-1)^{(n-2)\\\\cdots }}.}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51dbe91b0821c572570031f2a1b750ca24a17101" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.912ex; height:3.343ex;" alt="{\\\\displaystyle n^{(n-1)^{(n-2)\\\\cdots }}.}"></span></dd></dl> La factorielle exponentielle peut également être définie avec la relation de récurrence  <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 a_{0}=1,\\\\quad a_{n}=n^{a_{n-1}}.}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>0</mn>           </mrow>         </msub>         <mo>=</mo>         <mn>1</mn>         <mo>,</mo>         <mspace width="1em"></mspace>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msub>         <mo>=</mo>         <msup>           <mi>n</mi>           <mrow class="MJX-TeXAtom-ORD">             <msub>               <mi>a</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mi>n</mi>                 <mo>−<!-- − --></mo>                 <mn>1</mn>               </mrow>             </msub>           </mrow>         </msup>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{0}=1,\\\\quad a_{n}=n^{a_{n-1}}.}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12435f53186682f52518774c6e0e19bcf83b0b12" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.262ex; height:2.676ex;" alt="{\\\\displaystyle a_{0}=1,\\\\quad a_{n}=n^{a_{n-1}}.}"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Factorielle_exponentielle">https://fr.wikipedia.org/wiki/Factorielle_exponentielle</a>)"""@fr, """The <b>exponential factorial</b> is a positive integer <i>n</i> raised to the power of <i>n</i> − 1, which in turn is raised to the power of <i>n</i> − 2, and so on in a right-grouping manner. That is,  <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 n^{(n-1)^{(n-2)\\\\cdots }}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>n</mi>           <mrow class="MJX-TeXAtom-ORD">             <mo stretchy="false">(</mo>             <mi>n</mi>             <mo>−<!-- − --></mo>             <mn>1</mn>             <msup>               <mo stretchy="false">)</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mo stretchy="false">(</mo>                 <mi>n</mi>                 <mo>−<!-- − --></mo>                 <mn>2</mn>                 <mo stretchy="false">)</mo>                 <mo>⋯<!-- ⋯ --></mo>               </mrow>             </msup>           </mrow>         </msup>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle n^{(n-1)^{(n-2)\\\\cdots }}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ed45a0b09539b37aecbafee6faead7f1ee2d221" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.265ex; height:3.343ex;" alt="{\\\\displaystyle n^{(n-1)^{(n-2)\\\\cdots }}}"></span></dd></dl> The exponential factorial can also be defined with the recurrence relation  <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 a_{1}=1,\\\\quad a_{n}=n^{a_{n-1}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>1</mn>           </mrow>         </msub>         <mo>=</mo>         <mn>1</mn>         <mo>,</mo>         <mspace width="1em"></mspace>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msub>         <mo>=</mo>         <msup>           <mi>n</mi>           <mrow class="MJX-TeXAtom-ORD">             <msub>               <mi>a</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mi>n</mi>                 <mo>−<!-- − --></mo>                 <mn>1</mn>               </mrow>             </msub>           </mrow>         </msup>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{1}=1,\\\\quad a_{n}=n^{a_{n-1}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/685121e1e5d4e8e2d6d58e77a9865043ca6c6597" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.615ex; height:2.676ex;" alt="{\\\\displaystyle a_{1}=1,\\\\quad a_{n}=n^{a_{n-1}}}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Exponential_factorial">https://en.wikipedia.org/wiki/Exponential_factorial</a>)"""@en ;
  dc:created "2023-08-24"^^xsd:date ;
  skos:inScheme psr: .

psr:-FM1M1PDT-5
  skos:prefLabel "suite d'entiers"@fr, "integer sequence"@en ;
  a skos:Concept ;
  skos:narrower psr:-RT4H0VFD-8 .

psr:-BSS33T4W-C
  skos:prefLabel "grand nombre"@fr, "large number"@en ;
  a skos:Concept ;
  skos:narrower psr:-RT4H0VFD-8 .