@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:-K9FXDR6F-N
  skos:prefLabel "loi de probabilité"@fr, "probability distribution"@en ;
  a skos:Concept ;
  skos:narrower psr:-CNVQ7RKZ-P .

psr:-CNVQ7RKZ-P
  skos:prefLabel "fonction T d'Owen"@fr, "Owen's T function"@en ;
  a skos:Concept ;
  skos:definition """En mathématiques, la <b>fonction T d'Owen</b> <i>T</i>(<i>h</i>,&nbsp;<i>a</i>), du nom du statisticien Donald Bruce Owen, 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 T(h,a)={\\rac {1}{2\\\\pi }}\\\\int _{0}^{a}{\\rac {e^{-{\\rac {1}{2}}h^{2}(1+x^{2})}}{1+x^{2}}}\\\\,\\\\mathrm {d} x\\\\quad \\\\left(-\\\\infty <h,a<+\\\\infty \\
ight).}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>T</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>h</mi>
<br/>        <mo>,</mo>
<br/>        <mi>a</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mrow>
<br/>              <mn>2</mn>
<br/>              <mi>π<!-- π --></mi>
<br/>            </mrow>
<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>a</mi>
<br/>          </mrow>
<br/>        </msubsup>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <msup>
<br/>              <mi>e</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo>−<!-- − --></mo>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mfrac>
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<br/>                    <mn>2</mn>
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<br/>                <msup>
<br/>                  <mi>x</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mn>2</mn>
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<br/>                </msup>
<br/>                <mo stretchy="false">)</mo>
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<br/>            </msup>
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<br/>                  <mn>2</mn>
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<br/>              </msup>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="normal">d</mi>
<br/>        </mrow>
<br/>        <mi>x</mi>
<br/>        <mspace width="1em"></mspace>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>            <mo>&lt;</mo>
<br/>            <mi>h</mi>
<br/>            <mo>,</mo>
<br/>            <mi>a</mi>
<br/>            <mo>&lt;</mo>
<br/>            <mo>+</mo>
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle T(h,a)={\\rac {1}{2\\\\pi }}\\\\int _{0}^{a}{\\rac {e^{-{\\rac {1}{2}}h^{2}(1+x^{2})}}{1+x^{2}}}\\\\,\\\\mathrm {d} x\\\\quad \\\\left(-\\\\infty &lt;h,a&lt;+\\\\infty \\
ight).}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fcb4a62efe88c0ce288c2cd7a8f76b7e8f1594d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:56.307ex; height:7.176ex;" alt="{\\\\displaystyle T(h,a)={\\rac {1}{2\\\\pi }}\\\\int _{0}^{a}{\\rac {e^{-{\\rac {1}{2}}h^{2}(1+x^{2})}}{1+x^{2}}}\\\\,\\\\mathrm {d} x\\\\quad \\\\left(-\\\\infty <h,a<+\\\\infty \\
ight).}"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_T_d%27Owen">https://fr.wikipedia.org/wiki/Fonction_T_d%27Owen</a>)"""@fr, """In mathematics, <b>Owen's T function</b> <i>T</i>(<i>h</i>,&nbsp;<i>a</i>), named after statistician Donald Bruce Owen, is defined 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 T(h,a)={\\rac {1}{2\\\\pi }}\\\\int _{0}^{a}{\\rac {e^{-{\\rac {1}{2}}h^{2}(1+x^{2})}}{1+x^{2}}}dx\\\\quad \\\\left(-\\\\infty <h,a<+\\\\infty \\
ight).}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>T</mi>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>h</mi>
<br/>        <mo>,</mo>
<br/>        <mi>a</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mrow>
<br/>              <mn>2</mn>
<br/>              <mi>π<!-- π --></mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <msubsup>
<br/>          <mo>∫<!-- ∫ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
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<br/>        </msubsup>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <msup>
<br/>              <mi>e</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mo>−<!-- − --></mo>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mfrac>
<br/>                    <mn>1</mn>
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<br/>                  <mi>h</mi>
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<br/>                    <mn>2</mn>
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<br/>                </msup>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mn>1</mn>
<br/>                <mo>+</mo>
<br/>                <msup>
<br/>                  <mi>x</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mn>2</mn>
<br/>                  </mrow>
<br/>                </msup>
<br/>                <mo stretchy="false">)</mo>
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<br/>            </msup>
<br/>            <mrow>
<br/>              <mn>1</mn>
<br/>              <mo>+</mo>
<br/>              <msup>
<br/>                <mi>x</mi>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mn>2</mn>
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<br/>              </msup>
<br/>            </mrow>
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<br/>        </mrow>
<br/>        <mi>d</mi>
<br/>        <mi>x</mi>
<br/>        <mspace width="1em"></mspace>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>            <mo>&lt;</mo>
<br/>            <mi>h</mi>
<br/>            <mo>,</mo>
<br/>            <mi>a</mi>
<br/>            <mo>&lt;</mo>
<br/>            <mo>+</mo>
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
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<br/>          <mo>)</mo>
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<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle T(h,a)={\\rac {1}{2\\\\pi }}\\\\int _{0}^{a}{\\rac {e^{-{\\rac {1}{2}}h^{2}(1+x^{2})}}{1+x^{2}}}dx\\\\quad \\\\left(-\\\\infty &lt;h,a&lt;+\\\\infty \\
ight).}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1adc60372d2e4456c5fa476aab5573ae86370ed0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:55.843ex; height:7.176ex;" alt="{\\\\displaystyle T(h,a)={\\rac {1}{2\\\\pi }}\\\\int _{0}^{a}{\\rac {e^{-{\\rac {1}{2}}h^{2}(1+x^{2})}}{1+x^{2}}}dx\\\\quad \\\\left(-\\\\infty <h,a<+\\\\infty \\
ight).}"></span></dd></dl>
<br/>The function was first introduced by Owen in 1956.
<br/> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Owen%27s_T_function">https://en.wikipedia.org/wiki/Owen%27s_T_function</a>)"""@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_T_d%27Owen>, <https://en.wikipedia.org/wiki/Owen%27s_T_function> ;
  skos:broader psr:-K9FXDR6F-N, psr:-FH1H1FB9-1 ;
  dc:modified "2023-08-16"^^xsd:date ;
  skos:inScheme psr: ;
  dc:created "2023-08-16"^^xsd:date .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-CNVQ7RKZ-P .