@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:-PC9Q4CNL-L
  skos:definition """When solving the Helmholtz equation in spherical coordinates by separation of variables, the radial equation has the form
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle x^{2}{\\rac {d^{2}y}{dx^{2}}}+2x{\\rac {dy}{dx}}+\\\\left(x^{2}-n(n+1)\\
ight)y=0.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <msup>
<br/>                <mi>d</mi>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mn>2</mn>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mi>y</mi>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mi>d</mi>
<br/>              <msup>
<br/>                <mi>x</mi>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mn>2</mn>
<br/>                </mrow>
<br/>              </msup>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>+</mo>
<br/>        <mn>2</mn>
<br/>        <mi>x</mi>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>d</mi>
<br/>              <mi>y</mi>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mi>d</mi>
<br/>              <mi>x</mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>+</mo>
<br/>        <mrow>
<br/>          <mo>(</mo>
<br/>          <mrow>
<br/>            <msup>
<br/>              <mi>x</mi>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mn>2</mn>
<br/>              </mrow>
<br/>            </msup>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>n</mi>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>n</mi>
<br/>            <mo>+</mo>
<br/>            <mn>1</mn>
<br/>            <mo stretchy="false">)</mo>
<br/>          </mrow>
<br/>          <mo>)</mo>
<br/>        </mrow>
<br/>        <mi>y</mi>
<br/>        <mo>=</mo>
<br/>        <mn>0.</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle x^{2}{\\rac {d^{2}y}{dx^{2}}}+2x{\\rac {dy}{dx}}+\\\\left(x^{2}-n(n+1)\\
ight)y=0.}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/429ce6fc89762e92f4a2b77f264e33eca9f6179d" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -2.171ex; width:40.781ex; height:6.009ex;" alt="{\\\\displaystyle x^{2}{\\rac {d^{2}y}{dx^{2}}}+2x{\\rac {dy}{dx}}+\\\\left(x^{2}-n(n+1)\\
ight)y=0.}"></div>
<br/>The two linearly independent solutions to this equation are called the <b>spherical Bessel functions</b> <span class="texhtml mvar" style="font-style:italic;">j<sub>n</sub></span> and <span class="texhtml mvar" style="font-style:italic;">y<sub>n</sub></span>, and are related to the ordinary Bessel functions <span class="texhtml mvar" style="font-style:italic;">J<sub>n</sub></span> and <span class="texhtml mvar" style="font-style:italic;">Y<sub>n</sub></span> by
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\egin{aligned}j_{n}(x)&amp;={\\\\sqrt {\\rac {\\\\pi }{2x}}}J_{n+{\\rac {1}{2}}}(x),\\\\\\\\y_{n}(x)&amp;={\\\\sqrt {\\rac {\\\\pi }{2x}}}Y_{n+{\\rac {1}{2}}}(x)=(-1)^{n+1}{\\\\sqrt {\\rac {\\\\pi }{2x}}}J_{-n-{\\rac {1}{2}}}(x).\\\\end{aligned}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
<br/>            <mtr>
<br/>              <mtd>
<br/>                <msub>
<br/>                  <mi>j</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi></mi>
<br/>                <mo>=</mo>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <msqrt>
<br/>                    <mfrac>
<br/>                      <mi>π<!-- π --></mi>
<br/>                      <mrow>
<br/>                        <mn>2</mn>
<br/>                        <mi>x</mi>
<br/>                      </mrow>
<br/>                    </mfrac>
<br/>                  </msqrt>
<br/>                </mrow>
<br/>                <msub>
<br/>                  <mi>J</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                    <mo>+</mo>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mfrac>
<br/>                        <mn>1</mn>
<br/>                        <mn>2</mn>
<br/>                      </mfrac>
<br/>                    </mrow>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>                <mo>,</mo>
<br/>              </mtd>
<br/>            </mtr>
<br/>            <mtr>
<br/>              <mtd>
<br/>                <msub>
<br/>                  <mi>y</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi></mi>
<br/>                <mo>=</mo>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <msqrt>
<br/>                    <mfrac>
<br/>                      <mi>π<!-- π --></mi>
<br/>                      <mrow>
<br/>                        <mn>2</mn>
<br/>                        <mi>x</mi>
<br/>                      </mrow>
<br/>                    </mfrac>
<br/>                  </msqrt>
<br/>                </mrow>
<br/>                <msub>
<br/>                  <mi>Y</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                    <mo>+</mo>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mfrac>
<br/>                        <mn>1</mn>
<br/>                        <mn>2</mn>
<br/>                      </mfrac>
<br/>                    </mrow>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>                <mo>=</mo>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mo>−<!-- − --></mo>
<br/>                <mn>1</mn>
<br/>                <msup>
<br/>                  <mo stretchy="false">)</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                    <mo>+</mo>
<br/>                    <mn>1</mn>
<br/>                  </mrow>
<br/>                </msup>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <msqrt>
<br/>                    <mfrac>
<br/>                      <mi>π<!-- π --></mi>
<br/>                      <mrow>
<br/>                        <mn>2</mn>
<br/>                        <mi>x</mi>
<br/>                      </mrow>
<br/>                    </mfrac>
<br/>                  </msqrt>
<br/>                </mrow>
<br/>                <msub>
<br/>                  <mi>J</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mo>−<!-- − --></mo>
<br/>                    <mi>n</mi>
<br/>                    <mo>−<!-- − --></mo>
<br/>                    <mrow class="MJX-TeXAtom-ORD">
<br/>                      <mfrac>
<br/>                        <mn>1</mn>
<br/>                        <mn>2</mn>
<br/>                      </mfrac>
<br/>                    </mrow>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>                <mo>.</mo>
<br/>              </mtd>
<br/>            </mtr>
<br/>          </mtable>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\egin{aligned}j_{n}(x)&amp;={\\\\sqrt {\\rac {\\\\pi }{2x}}}J_{n+{\\rac {1}{2}}}(x),\\\\\\\\y_{n}(x)&amp;={\\\\sqrt {\\rac {\\\\pi }{2x}}}Y_{n+{\\rac {1}{2}}}(x)=(-1)^{n+1}{\\\\sqrt {\\rac {\\\\pi }{2x}}}J_{-n-{\\rac {1}{2}}}(x).\\\\end{aligned}}}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12c926045bde27cc3fba1446d408edd029802ddb" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -5.671ex; width:50.693ex; height:12.509ex;" alt="{\\\\displaystyle {\\egin{aligned}j_{n}(x)&amp;={\\\\sqrt {\\rac {\\\\pi }{2x}}}J_{n+{\\rac {1}{2}}}(x),\\\\\\\\y_{n}(x)&amp;={\\\\sqrt {\\rac {\\\\pi }{2x}}}Y_{n+{\\rac {1}{2}}}(x)=(-1)^{n+1}{\\\\sqrt {\\rac {\\\\pi }{2x}}}J_{-n-{\\rac {1}{2}}}(x).\\\\end{aligned}}}"></div>
<br/><span class="texhtml mvar" style="font-style:italic;">y<sub>n</sub></span> is also denoted <span class="texhtml mvar" style="font-style:italic;">n<sub>n</sub></span> or <span class="texhtml mvar" style="font-style:italic;">η<sub>n</sub></span>; some authors call these functions the <b>spherical Neumann functions</b>.
<br/>From the relations to the ordinary Bessel functions it is directly seen that:
<br/><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 {\\egin{aligned}j_{n}(x)&amp;=(-1)^{n}y_{-n-1}(x)\\\\\\\\y_{n}(x)&amp;=(-1)^{n+1}j_{-n-1}(x)\\\\end{aligned}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
<br/>            <mtr>
<br/>              <mtd>
<br/>                <msub>
<br/>                  <mi>j</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi></mi>
<br/>                <mo>=</mo>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mo>−<!-- − --></mo>
<br/>                <mn>1</mn>
<br/>                <msup>
<br/>                  <mo stretchy="false">)</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                  </mrow>
<br/>                </msup>
<br/>                <msub>
<br/>                  <mi>y</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mo>−<!-- − --></mo>
<br/>                    <mi>n</mi>
<br/>                    <mo>−<!-- − --></mo>
<br/>                    <mn>1</mn>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>              </mtd>
<br/>            </mtr>
<br/>            <mtr>
<br/>              <mtd>
<br/>                <msub>
<br/>                  <mi>y</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi></mi>
<br/>                <mo>=</mo>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mo>−<!-- − --></mo>
<br/>                <mn>1</mn>
<br/>                <msup>
<br/>                  <mo stretchy="false">)</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>n</mi>
<br/>                    <mo>+</mo>
<br/>                    <mn>1</mn>
<br/>                  </mrow>
<br/>                </msup>
<br/>                <msub>
<br/>                  <mi>j</mi>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mo>−<!-- − --></mo>
<br/>                    <mi>n</mi>
<br/>                    <mo>−<!-- − --></mo>
<br/>                    <mn>1</mn>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo stretchy="false">(</mo>
<br/>                <mi>x</mi>
<br/>                <mo stretchy="false">)</mo>
<br/>              </mtd>
<br/>            </mtr>
<br/>          </mtable>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\egin{aligned}j_{n}(x)&amp;=(-1)^{n}y_{-n-1}(x)\\\\\\\\y_{n}(x)&amp;=(-1)^{n+1}j_{-n-1}(x)\\\\end{aligned}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/929a7d455d74a5f1ff3ec368e8de0b4608d0e30b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:26.14ex; height:6.176ex;" alt="{\\\\displaystyle {\\egin{aligned}j_{n}(x)&amp;=(-1)^{n}y_{-n-1}(x)\\\\\\\\y_{n}(x)&amp;=(-1)^{n+1}j_{-n-1}(x)\\\\end{aligned}}}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Bessel_function#Spherical_Bessel_functions">https://en.wikipedia.org/wiki/Bessel_function#Spherical_Bessel_functions</a>)"""@en, """En analyse, les <b>fonctions de Bessel sphériques</b> sont des fonctions spéciales construites à partir des fonctions de Bessel classiques et qui interviennent dans certains problèmes possédant une symétrie sphérique.
<br/>Elles sont définies par&nbsp;:
<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 j_{n}(x)={\\\\sqrt {\\\\pi  \\\\over 2x}}J_{n+{1 \\\\over 2}}(x),}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>j</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <msqrt>
<br/>            <mfrac>
<br/>              <mi>π<!-- π --></mi>
<br/>              <mrow>
<br/>                <mn>2</mn>
<br/>                <mi>x</mi>
<br/>              </mrow>
<br/>            </mfrac>
<br/>          </msqrt>
<br/>        </mrow>
<br/>        <msub>
<br/>          <mi>J</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>+</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mn>1</mn>
<br/>                <mn>2</mn>
<br/>              </mfrac>
<br/>            </mrow>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle j_{n}(x)={\\\\sqrt {\\\\pi  \\\\over 2x}}J_{n+{1 \\\\over 2}}(x),}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ead8423eda6c6d00bf12351e2e8bb1e1a12fe09" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.027ex; width:23.169ex; height:6.343ex;" alt="{\\\\displaystyle j_{n}(x)={\\\\sqrt {\\\\pi  \\\\over 2x}}J_{n+{1 \\\\over 2}}(x),}"></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 y_{n}(x)={\\\\sqrt {\\\\pi  \\\\over 2x}}Y_{n+{1 \\\\over 2}}(x)=(-1)^{n+1}{\\\\sqrt {\\\\pi  \\\\over 2x}}J_{-n-{\\rac {1}{2}}}(x).}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <msqrt>
<br/>            <mfrac>
<br/>              <mi>π<!-- π --></mi>
<br/>              <mrow>
<br/>                <mn>2</mn>
<br/>                <mi>x</mi>
<br/>              </mrow>
<br/>            </mfrac>
<br/>          </msqrt>
<br/>        </mrow>
<br/>        <msub>
<br/>          <mi>Y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>+</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mn>1</mn>
<br/>                <mn>2</mn>
<br/>              </mfrac>
<br/>            </mrow>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mn>1</mn>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>+</mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <msqrt>
<br/>            <mfrac>
<br/>              <mi>π<!-- π --></mi>
<br/>              <mrow>
<br/>                <mn>2</mn>
<br/>                <mi>x</mi>
<br/>              </mrow>
<br/>            </mfrac>
<br/>          </msqrt>
<br/>        </mrow>
<br/>        <msub>
<br/>          <mi>J</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>n</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mn>1</mn>
<br/>                <mn>2</mn>
<br/>              </mfrac>
<br/>            </mrow>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle y_{n}(x)={\\\\sqrt {\\\\pi  \\\\over 2x}}Y_{n+{1 \\\\over 2}}(x)=(-1)^{n+1}{\\\\sqrt {\\\\pi  \\\\over 2x}}J_{-n-{\\rac {1}{2}}}(x).}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71d796cf93127a37408376bb7d7399516b5208bf" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:49.942ex; height:6.343ex;" alt="{\\\\displaystyle y_{n}(x)={\\\\sqrt {\\\\pi  \\\\over 2x}}Y_{n+{1 \\\\over 2}}(x)=(-1)^{n+1}{\\\\sqrt {\\\\pi  \\\\over 2x}}J_{-n-{\\rac {1}{2}}}(x).}"></span></dd></dl>
<br/>En particulier, <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 j_{0}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>j</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle j_{0}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7829ecaa6c8e08ce2a635f4d0232b6ac68a81f8" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:2.039ex; height:2.509ex;" alt="j_{0}"></span> correspond à la fonction sinus cardinal&nbsp;:
<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 j_{0}(x)={\\
m {sinc}}(x)={\\\\sin(x) \\\\over x}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>j</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">s</mi>
<br/>            <mi mathvariant="normal">i</mi>
<br/>            <mi mathvariant="normal">n</mi>
<br/>            <mi mathvariant="normal">c</mi>
<br/>          </mrow>
<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/>            <mrow>
<br/>              <mi>sin</mi>
<br/>              <mo>⁡<!-- ⁡ --></mo>
<br/>              <mo stretchy="false">(</mo>
<br/>              <mi>x</mi>
<br/>              <mo stretchy="false">)</mo>
<br/>            </mrow>
<br/>            <mi>x</mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle j_{0}(x)={\\
m {sinc}}(x)={\\\\sin(x) \\\\over x}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f606f8dfb704331151fd1454cf8d7c3ae1d10cf1" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.027ex; width:25.879ex; height:5.676ex;" alt="{\\\\displaystyle j_{0}(x)={\\
m {sinc}}(x)={\\\\sin(x) \\\\over x}.}"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_de_Bessel_sph%C3%A9rique">https://fr.wikipedia.org/wiki/Fonction_de_Bessel_sph%C3%A9rique</a>)"""@fr ;
  dc:modified "2023-07-27"^^xsd:date ;
  skos:prefLabel "spherical Bessel function"@en, "fonction de Bessel sphérique"@fr ;
  skos:inScheme psr: ;
  a skos:Concept ;
  dc:created "2023-07-27"^^xsd:date ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Bessel_function#Spherical_Bessel_functions>, <https://fr.wikipedia.org/wiki/Fonction_de_Bessel_sph%C3%A9rique> ;
  skos:broader psr:-FH1H1FB9-1 .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-PC9Q4CNL-L .