@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:-GND317C1-S
  skos:exactMatch <https://en.wikipedia.org/wiki/Bateman_function> ;
  dc:modified "2023-08-17"^^xsd:date ;
  dc:created "2023-08-17"^^xsd:date ;
  skos:altLabel "k-function"@en ;
  a skos:Concept ;
  skos:broader psr:-VZ83B143-L ;
  skos:definition """In mathematics, the <b>Bateman function</b> (or <i>k</i>-function)  is a special case of the confluent hypergeometric function studied by Harry Bateman(1931).  Bateman defined it by
<br/>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\displaystyle k_{n}(x)={\\rac {2}{\\\\pi }}\\\\int _{0}^{\\\\pi /2}\\\\cos(x\\	an \\	heta -n\\	heta )\\\\,d\\	heta }</annotation>
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<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55f40a7e9dca59222c85200d43db9ad020f168ae" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:36.385ex; height:6.343ex;" alt="\\\\displaystyle k_{n}(x)={\\rac  {2}{\\\\pi }}\\\\int _{0}^{{\\\\pi /2}}\\\\cos(x\\	an \\	heta -n\\	heta )\\\\,d\\	heta "></span></dd></dl>
<br/>Bateman discovered this function, when Theodore von Kármán asked for the solution of the following differential equation which appeared in the theory of turbulence
<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 x{\\rac {d^{2}u}{dx^{2}}}=(x-n)u}">
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<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37874b185b0eaf6c407d19741da25886c5a0b526" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.171ex; width:17.57ex; height:6.009ex;" alt="{\\\\displaystyle x{\\rac {d^{2}u}{dx^{2}}}=(x-n)u}"></span></dd></dl>
<br/>and Bateman found this function as one of the solutions. Bateman denoted this function as "k" function in honor of Theodore von Kármán. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Bateman_function">https://en.wikipedia.org/wiki/Bateman_function</a>)"""@en ;
  skos:inScheme psr: ;
  skos:prefLabel "Bateman function"@en, "fonction de Bateman"@fr .

psr:-VZ83B143-L
  skos:prefLabel "fonction hypergéométrique"@fr, "hypergeometric function"@en ;
  a skos:Concept ;
  skos:narrower psr:-GND317C1-S .