@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:-Q7FKCBLQ-N
  skos:definition """In mathematics, the <b>Scorer's functions</b> are special functions studied by Scorer (1950) and denoted Gi(<i>x</i>) and Hi(<i>x</i>). 
<br/>Hi(<i>x</i>) and -Gi(<i>x</i>) solve the equation 
<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 y''(x)-x\\\\ y(x)={\\rac {1}{\\\\pi }}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>y</mi>
<br/>          <mo>″</mo>
<br/>        </msup>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mi>x</mi>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <mi>y</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mi>π<!-- π --></mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle y''(x)-x\\\\ y(x)={\\rac {1}{\\\\pi }}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb006d96b6e5829467525fbe49b19b1673c39cf9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:19.748ex; height:5.176ex;" alt="{\\\\displaystyle y''(x)-x\\\\ y(x)={\\rac {1}{\\\\pi }}}"></span></dd></dl>
<br/>and are 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 \\\\mathrm {Gi} (x)={\\rac {1}{\\\\pi }}\\\\int _{0}^{\\\\infty }\\\\sin \\\\left({\\rac {t^{3}}{3}}+xt\\
ight)\\\\,dt,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="normal">G</mi>
<br/>          <mi mathvariant="normal">i</mi>
<br/>        </mrow>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mi>π<!-- π --></mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <msubsup>
<br/>          <mo>∫<!-- ∫ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mi>sin</mi>
<br/>        <mo>⁡<!-- ⁡ --></mo>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <msup>
<br/>                  <mi>t</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mn>3</mn>
<br/>                  </mrow>
<br/>                </msup>
<br/>                <mn>3</mn>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <mo>+</mo>
<br/>            <mi>x</mi>
<br/>            <mi>t</mi>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mi>d</mi>
<br/>        <mi>t</mi>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {Gi} (x)={\\rac {1}{\\\\pi }}\\\\int _{0}^{\\\\infty }\\\\sin \\\\left({\\rac {t^{3}}{3}}+xt\\
ight)\\\\,dt,}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df49a386e80f5c74ad7446072bd88b39023807b4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:33.096ex; height:6.343ex;" alt="{\\\\displaystyle \\\\mathrm {Gi} (x)={\\rac {1}{\\\\pi }}\\\\int _{0}^{\\\\infty }\\\\sin \\\\left({\\rac {t^{3}}{3}}+xt\\
ight)\\\\,dt,}"></span></dd>
<br/><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 \\\\mathrm {Hi} (x)={\\rac {1}{\\\\pi }}\\\\int _{0}^{\\\\infty }\\\\exp \\\\left(-{\\rac {t^{3}}{3}}+xt\\
ight)\\\\,dt.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="normal">H</mi>
<br/>          <mi mathvariant="normal">i</mi>
<br/>        </mrow>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mi>π<!-- π --></mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <msubsup>
<br/>          <mo>∫<!-- ∫ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mi>exp</mi>
<br/>        <mo>⁡<!-- ⁡ --></mo>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <msup>
<br/>                  <mi>t</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mn>3</mn>
<br/>                  </mrow>
<br/>                </msup>
<br/>                <mn>3</mn>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <mo>+</mo>
<br/>            <mi>x</mi>
<br/>            <mi>t</mi>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mi>d</mi>
<br/>        <mi>t</mi>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {Hi} (x)={\\rac {1}{\\\\pi }}\\\\int _{0}^{\\\\infty }\\\\exp \\\\left(-{\\rac {t^{3}}{3}}+xt\\
ight)\\\\,dt.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fad3438a7af8466f97f0bc017ee3bbd828a37f3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:35.52ex; height:6.343ex;" alt="{\\\\displaystyle \\\\mathrm {Hi} (x)={\\rac {1}{\\\\pi }}\\\\int _{0}^{\\\\infty }\\\\exp \\\\left(-{\\rac {t^{3}}{3}}+xt\\
ight)\\\\,dt.}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Scorer%27s_function">https://en.wikipedia.org/wiki/Scorer%27s_function</a>)"""@en, """Les fonctions de Scorer (du nom du mathématicien R. S. Scorer) sont des fonctions spéciales notées Gi(<i>x</i>) et Hi(<i>x</i>). 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_de_Scorer">https://fr.wikipedia.org/wiki/Fonction_de_Scorer</a>)"""@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_de_Scorer>, <https://en.wikipedia.org/wiki/Scorer%27s_function> ;
  skos:broader psr:-FH1H1FB9-1 ;
  skos:inScheme psr: ;
  skos:prefLabel "fonction de Scorer"@fr, "Scorer's function"@en ;
  a skos:Concept ;
  dc:created "2023-08-16"^^xsd:date ;
  dc:modified "2023-08-16"^^xsd:date .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-Q7FKCBLQ-N .