@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:-FWTTZ9R7-X
  skos:prefLabel "fonction numérique à plusieurs variables réelles"@fr, "function of several real variables"@en ;
  a skos:Concept ;
  skos:narrower psr:-NXX2Z7NJ-R .

psr: a skos:ConceptScheme .
psr:-NXX2Z7NJ-R
  a skos:Concept ;
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  skos:definition """En mathématiques, la <b>fonction de Kampé de Fériet</b> est une fonction hypergéométrique d'ordre supérieur à deux variables. Elle constitue généralisation à deux variables des séries hypergéométriques introduites par Joseph Kampé de Fériet et Paul Appell.
<br/>La fonction hypergéométrique de Kampé de Fériet est définie par
<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 {}^{p+q}f_{r+s}\\\\left({\\egin{matrix}a_{1},\\\\cdots ,a_{p}\\\\colon b_{1},b_{1}{}';\\\\cdots ;b_{q},b_{q}{}';\\\\\\\\c_{1},\\\\cdots ,c_{r}\\\\colon d_{1},d_{1}{}';\\\\cdots ;d_{s},d_{s}{}';\\\\end{matrix}}x,y\\
ight)=\\\\sum _{m=0}^{\\\\infty }\\\\sum _{n=0}^{\\\\infty }{\\rac {(a_{1})_{m+n}\\\\cdots (a_{p})_{m+n}}{(c_{1})_{m+n}\\\\cdots (c_{r})_{m+n}}}{\\rac {(b_{1})_{m}(b_{1}{}')_{n}\\\\cdots (b_{q})_{m}(b_{q}{}')_{n}}{(d_{1})_{m}(d_{1}{}')_{n}\\\\cdots (d_{s})_{m}(d_{s}{}')_{n}}}\\\\cdot {\\rac {x^{m}y^{n}}{m!n!}}.}">
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {}^{p+q}f_{r+s}\\\\left({\\egin{matrix}a_{1},\\\\cdots ,a_{p}\\\\colon b_{1},b_{1}{}';\\\\cdots ;b_{q},b_{q}{}';\\\\\\\\c_{1},\\\\cdots ,c_{r}\\\\colon d_{1},d_{1}{}';\\\\cdots ;d_{s},d_{s}{}';\\\\end{matrix}}x,y\\
ight)=\\\\sum _{m=0}^{\\\\infty }\\\\sum _{n=0}^{\\\\infty }{\\rac {(a_{1})_{m+n}\\\\cdots (a_{p})_{m+n}}{(c_{1})_{m+n}\\\\cdots (c_{r})_{m+n}}}{\\rac {(b_{1})_{m}(b_{1}{}')_{n}\\\\cdots (b_{q})_{m}(b_{q}{}')_{n}}{(d_{1})_{m}(d_{1}{}')_{n}\\\\cdots (d_{s})_{m}(d_{s}{}')_{n}}}\\\\cdot {\\rac {x^{m}y^{n}}{m!n!}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fe52f472fad21edef790f28d9d4790274c49d53" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; margin-left: -0.063ex; width:111.265ex; height:6.843ex;" alt="{\\\\displaystyle {}^{p+q}f_{r+s}\\\\left({\\egin{matrix}a_{1},\\\\cdots ,a_{p}\\\\colon b_{1},b_{1}{}';\\\\cdots ;b_{q},b_{q}{}';\\\\\\\\c_{1},\\\\cdots ,c_{r}\\\\colon d_{1},d_{1}{}';\\\\cdots ;d_{s},d_{s}{}';\\\\end{matrix}}x,y\\
ight)=\\\\sum _{m=0}^{\\\\infty }\\\\sum _{n=0}^{\\\\infty }{\\rac {(a_{1})_{m+n}\\\\cdots (a_{p})_{m+n}}{(c_{1})_{m+n}\\\\cdots (c_{r})_{m+n}}}{\\rac {(b_{1})_{m}(b_{1}{}')_{n}\\\\cdots (b_{q})_{m}(b_{q}{}')_{n}}{(d_{1})_{m}(d_{1}{}')_{n}\\\\cdots (d_{s})_{m}(d_{s}{}')_{n}}}\\\\cdot {\\rac {x^{m}y^{n}}{m!n!}}.}"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_de_Kamp%C3%A9_de_F%C3%A9riet">https://fr.wikipedia.org/wiki/Fonction_de_Kamp%C3%A9_de_F%C3%A9riet</a>)"""@fr, """In mathematics, the <b>Kampé de Fériet function</b> is a two-variable generalization of the generalized hypergeometric series, introduced by Joseph Kampé de Fériet.
<br/>The Kampé de Fériet function is given by
<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 {}^{p+q}F_{r+s}\\\\left({\\egin{matrix}a_{1},\\\\cdots ,a_{p}\\\\colon b_{1},b_{1}{}';\\\\cdots ;b_{q},b_{q}{}';\\\\\\\\c_{1},\\\\cdots ,c_{r}\\\\colon d_{1},d_{1}{}';\\\\cdots ;d_{s},d_{s}{}';\\\\end{matrix}}x,y\\
ight)=\\\\sum _{m=0}^{\\\\infty }\\\\sum _{n=0}^{\\\\infty }{\\rac {(a_{1})_{m+n}\\\\cdots (a_{p})_{m+n}}{(c_{1})_{m+n}\\\\cdots (c_{r})_{m+n}}}{\\rac {(b_{1})_{m}(b_{1}{}')_{n}\\\\cdots (b_{q})_{m}(b_{q}{}')_{n}}{(d_{1})_{m}(d_{1}{}')_{n}\\\\cdots (d_{s})_{m}(d_{s}{}')_{n}}}\\\\cdot {\\rac {x^{m}y^{n}}{m!n!}}.}">
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {}^{p+q}F_{r+s}\\\\left({\\egin{matrix}a_{1},\\\\cdots ,a_{p}\\\\colon b_{1},b_{1}{}';\\\\cdots ;b_{q},b_{q}{}';\\\\\\\\c_{1},\\\\cdots ,c_{r}\\\\colon d_{1},d_{1}{}';\\\\cdots ;d_{s},d_{s}{}';\\\\end{matrix}}x,y\\
ight)=\\\\sum _{m=0}^{\\\\infty }\\\\sum _{n=0}^{\\\\infty }{\\rac {(a_{1})_{m+n}\\\\cdots (a_{p})_{m+n}}{(c_{1})_{m+n}\\\\cdots (c_{r})_{m+n}}}{\\rac {(b_{1})_{m}(b_{1}{}')_{n}\\\\cdots (b_{q})_{m}(b_{q}{}')_{n}}{(d_{1})_{m}(d_{1}{}')_{n}\\\\cdots (d_{s})_{m}(d_{s}{}')_{n}}}\\\\cdot {\\rac {x^{m}y^{n}}{m!n!}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60efb0060f35d6db995bd00d893b7597319a0d9b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; margin-left: -0.063ex; width:111.62ex; height:6.843ex;" alt="{\\\\displaystyle {}^{p+q}F_{r+s}\\\\left({\\egin{matrix}a_{1},\\\\cdots ,a_{p}\\\\colon b_{1},b_{1}{}';\\\\cdots ;b_{q},b_{q}{}';\\\\\\\\c_{1},\\\\cdots ,c_{r}\\\\colon d_{1},d_{1}{}';\\\\cdots ;d_{s},d_{s}{}';\\\\end{matrix}}x,y\\
ight)=\\\\sum _{m=0}^{\\\\infty }\\\\sum _{n=0}^{\\\\infty }{\\rac {(a_{1})_{m+n}\\\\cdots (a_{p})_{m+n}}{(c_{1})_{m+n}\\\\cdots (c_{r})_{m+n}}}{\\rac {(b_{1})_{m}(b_{1}{}')_{n}\\\\cdots (b_{q})_{m}(b_{q}{}')_{n}}{(d_{1})_{m}(d_{1}{}')_{n}\\\\cdots (d_{s})_{m}(d_{s}{}')_{n}}}\\\\cdot {\\rac {x^{m}y^{n}}{m!n!}}.}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Kamp%C3%A9_de_F%C3%A9riet_function">https://en.wikipedia.org/wiki/Kamp%C3%A9_de_F%C3%A9riet_function</a>)"""@en ;
  dc:created "2023-07-26"^^xsd:date ;
  skos:prefLabel "fonction de Kampé de Fériet"@fr, "Kampé de Fériet function"@en ;
  skos:broader psr:-FWTTZ9R7-X, psr:-VZ83B143-L ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_de_Kamp%C3%A9_de_F%C3%A9riet>, <https://en.wikipedia.org/wiki/Kamp%C3%A9_de_F%C3%A9riet_function> ;
  dc:modified "2023-07-26"^^xsd:date .

psr:-VZ83B143-L
  skos:prefLabel "fonction hypergéométrique"@fr, "hypergeometric function"@en ;
  a skos:Concept ;
  skos:narrower psr:-NXX2Z7NJ-R .