Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.2133.59 on revision:2133

* Page found: Multipolstrahlung (eq math.2133.59)

(force rerendering)

Occurrences on the following pages:

Hash: aec03f88abb64b84a0682b9a9f1923ea

TeX (original user input): 

\bar{\bar{Q}}\left( \tau  \right)=\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }\rho \left( \bar{r}\acute{\ },\tau  \right)}\left( 3\bar{r}\acute{\ }\otimes \bar{r}\acute{\ }-r{{\acute{\ }}^{2}}\bar{\bar{1}} \right)=:\tilde{\bar{\bar{Q}}}-\frac{1}{3}\left( tr\left( {\tilde{\bar{\bar{Q}}}} \right) \right)\bar{\bar{1}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (15.902 KB / 2.293 KB) :

Q ¯ ¯ ( τ ) = ∫ d 3 r ´ ρ ( r ¯ ´ , τ ) ( 3 r ¯ ´ ⊗ r ¯ ´ - r ´ 2 1 ¯ ¯ ) = : Q ¯ ¯ ~ - 1 3 ( t r ( Q ¯ ¯ ~ ) ) 1 ¯ ¯ fragments ¯ ¯ 𝑄 fragments ( τ ) superscript 𝑑 3 r ´ absent ρ fragments ( ¯ 𝑟 ´ absent , τ ) fragments ( 3 ¯ 𝑟 ´ absent tensor-product ¯ 𝑟 ´ absent r superscript ´ absent 2 ¯ ¯ 1 ) : ~ ¯ ¯ 𝑄 1 3 fragments ( t r fragments ( ~ ¯ ¯ 𝑄 ) ) ¯ ¯ 1 {\displaystyle{\displaystyle\bar{\bar{Q}}\left(\tau\right)=\int{{{d}^{3}}r% \acute{\ }\rho\left(\bar{r}\acute{\ },\tau\right)}\left(3\bar{r}\acute{\ }% \otimes\bar{r}\acute{\ }-r{{\acute{\ }}^{2}}\bar{\bar{1}}\right)=:\tilde{\bar{% \bar{Q}}}-\frac{1}{3}\left(tr\left({\tilde{\bar{\bar{Q}}}}\right)\right)\bar{% \bar{1}}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\bar{\bar{Q}}\left(\tau\right)=\int{{{d}^{3}}r%&#10;\acute{\ }\rho\left(\bar{r}\acute{\ },\tau\right)}\left(3\bar{r}\acute{\ }%&#10;\otimes\bar{r}\acute{\ }-r{{\acute{\ }}^{2}}\bar{\bar{1}}\right)=:\tilde{\bar{%&#10;\bar{Q}}}-\frac{1}{3}\left(tr\left({\tilde{\bar{\bar{Q}}}}\right)\right)\bar{%&#10;\bar{1}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mover accent="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
        <mover accent="true" id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">
          <mi id="p1.1.m1.1.1.2.1.2" xref="p1.1.m1.1.1.2.1.2.cmml">Q</mi>
          <mo stretchy="false" id="p1.1.m1.1.1.2.1.1" xref="p1.1.m1.1.1.2.1.1.cmml">¯</mo>
        </mover>
        <mo stretchy="false" id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">¯</mo>
      </mover>
      <mrow id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
        <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">(</mo>
        <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">τ</mi>
        <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
      <mstyle displaystyle="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
        <mo largeop="true" symmetric="true" id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">∫</mo>
      </mstyle>
      <msup id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">
        <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">d</mi>
        <mn id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">3</mn>
      </msup>
      <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">r</mi>
      <mover accent="true" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
        <mi id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml"/>
        <mo id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">´</mo>
      </mover>
      <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">ρ</mi>
      <mrow id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">
        <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">(</mo>
        <mover accent="true" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
          <mi id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">r</mi>
          <mo stretchy="false" id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">¯</mo>
        </mover>
        <mover accent="true" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
          <mi id="p1.1.m1.1.14.2" xref="p1.1.m1.1.14.2.cmml"/>
          <mo id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">´</mo>
        </mover>
        <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">,</mo>
        <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">τ</mi>
        <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">)</mo>
      </mrow>
      <mrow id="p1.1.m1.1.46" xref="p1.1.m1.1.46.cmml">
        <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">(</mo>
        <mn id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">3</mn>
        <mover accent="true" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
          <mi id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">r</mi>
          <mo stretchy="false" id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">¯</mo>
        </mover>
        <mover accent="true" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
          <mi id="p1.1.m1.1.21.2" xref="p1.1.m1.1.21.2.cmml"/>
          <mo id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">´</mo>
        </mover>
        <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">⊗</mo>
        <mover accent="true" id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
          <mi id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.cmml">r</mi>
          <mo stretchy="false" id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">¯</mo>
        </mover>
        <mover accent="true" id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">
          <mi id="p1.1.m1.1.24.2" xref="p1.1.m1.1.24.2.cmml"/>
          <mo id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">´</mo>
        </mover>
        <mo id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">-</mo>
        <mi id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">r</mi>
        <msup id="p1.1.m1.1.45" xref="p1.1.m1.1.45.cmml">
          <mover accent="true" id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">
            <mi id="p1.1.m1.1.27.2" xref="p1.1.m1.1.27.2.cmml"/>
            <mo id="p1.1.m1.1.27.1" xref="p1.1.m1.1.27.1.cmml">´</mo>
          </mover>
          <mn id="p1.1.m1.1.28.1" xref="p1.1.m1.1.28.1.cmml">2</mn>
        </msup>
        <mover accent="true" id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">
          <mover accent="true" id="p1.1.m1.1.29.2" xref="p1.1.m1.1.29.2.cmml">
            <mn id="p1.1.m1.1.29.2.1.2" xref="p1.1.m1.1.29.2.1.2.cmml">1</mn>
            <mo stretchy="false" id="p1.1.m1.1.29.2.1.1" xref="p1.1.m1.1.29.2.1.1.cmml">¯</mo>
          </mover>
          <mo stretchy="false" id="p1.1.m1.1.29.1" xref="p1.1.m1.1.29.1.cmml">¯</mo>
        </mover>
        <mo id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">=</mo>
      <mo id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">:</mo>
      <mover accent="true" id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">
        <mover accent="true" id="p1.1.m1.1.33.2" xref="p1.1.m1.1.33.2.cmml">
          <mover accent="true" id="p1.1.m1.1.33.2.1.2" xref="p1.1.m1.1.33.2.1.2.cmml">
            <mi id="p1.1.m1.1.33.2.1.2.1.2" xref="p1.1.m1.1.33.2.1.2.1.2.cmml">Q</mi>
            <mo stretchy="false" id="p1.1.m1.1.33.2.1.2.1.1" xref="p1.1.m1.1.33.2.1.2.1.1.cmml">¯</mo>
          </mover>
          <mo stretchy="false" id="p1.1.m1.1.33.2.1.1" xref="p1.1.m1.1.33.2.1.1.cmml">¯</mo>
        </mover>
        <mo stretchy="false" id="p1.1.m1.1.33.1" xref="p1.1.m1.1.33.1.cmml">~</mo>
      </mover>
      <mo id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">-</mo>
      <mstyle displaystyle="true" id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">
        <mfrac id="p1.1.m1.1.35a" xref="p1.1.m1.1.35.cmml">
          <mn id="p1.1.m1.1.35.2" xref="p1.1.m1.1.35.2.cmml">1</mn>
          <mn id="p1.1.m1.1.35.3" xref="p1.1.m1.1.35.3.cmml">3</mn>
        </mfrac>
      </mstyle>
      <mrow id="p1.1.m1.1.48" xref="p1.1.m1.1.48.cmml">
        <mo id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">(</mo>
        <mi id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">t</mi>
        <mi id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">r</mi>
        <mrow id="p1.1.m1.1.47" xref="p1.1.m1.1.47.cmml">
          <mo id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">(</mo>
          <mover accent="true" id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">
            <mover accent="true" id="p1.1.m1.1.40.2" xref="p1.1.m1.1.40.2.cmml">
              <mover accent="true" id="p1.1.m1.1.40.2.1.2" xref="p1.1.m1.1.40.2.1.2.cmml">
                <mi id="p1.1.m1.1.40.2.1.2.1.2" xref="p1.1.m1.1.40.2.1.2.1.2.cmml">Q</mi>
                <mo stretchy="false" id="p1.1.m1.1.40.2.1.2.1.1" xref="p1.1.m1.1.40.2.1.2.1.1.cmml">¯</mo>
              </mover>
              <mo stretchy="false" id="p1.1.m1.1.40.2.1.1" xref="p1.1.m1.1.40.2.1.1.cmml">¯</mo>
            </mover>
            <mo stretchy="false" id="p1.1.m1.1.40.1" xref="p1.1.m1.1.40.1.cmml">~</mo>
          </mover>
          <mo id="p1.1.m1.1.41" xref="p1.1.m1.1.41.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">)</mo>
      </mrow>
      <mover accent="true" id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">
        <mover accent="true" id="p1.1.m1.1.43.2" xref="p1.1.m1.1.43.2.cmml">
          <mn id="p1.1.m1.1.43.2.1.2" xref="p1.1.m1.1.43.2.1.2.cmml">1</mn>
          <mo stretchy="false" id="p1.1.m1.1.43.2.1.1" xref="p1.1.m1.1.43.2.1.1.cmml">¯</mo>
        </mover>
        <mo stretchy="false" id="p1.1.m1.1.43.1" xref="p1.1.m1.1.43.1.cmml">¯</mo>
      </mover>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
          <ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">¯</ci>
          <apply id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">
            <ci id="p1.1.m1.1.1.2.1.1.cmml" xref="p1.1.m1.1.1.2.1.1">¯</ci>
            <ci id="p1.1.m1.1.1.2.1.2.cmml" xref="p1.1.m1.1.1.2.1.2">𝑄</ci>
          </apply>
        </apply>
        <cerror id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
          <csymbol cd="ambiguous" id="p1.1.m1.1.8a.cmml" xref="p1.1.m1.1.8">fragments</csymbol>
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">τ</csymbol>
          <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">)</ci>
        </cerror>
        <eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
        <int id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
        <apply id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44">
          <csymbol cd="ambiguous" id="p1.1.m1.1.44.1.cmml" xref="p1.1.m1.1.44">superscript</csymbol>
          <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝑑</ci>
          <cn type="integer" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">3</cn>
        </apply>
        <csymbol cd="unknown" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">r</csymbol>
        <apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
          <ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">´</ci>
          <csymbol cd="latexml" id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2">absent</csymbol>
        </apply>
        <csymbol cd="unknown" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">ρ</csymbol>
        <cerror id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">
          <csymbol cd="ambiguous" id="p1.1.m1.1.28a.cmml" xref="p1.1.m1.1.28">fragments</csymbol>
          <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">(</ci>
          <apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
            <ci id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">¯</ci>
            <ci id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">𝑟</ci>
          </apply>
          <apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
            <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">´</ci>
            <csymbol cd="latexml" id="p1.1.m1.1.14.2.cmml" xref="p1.1.m1.1.14.2">absent</csymbol>
          </apply>
          <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">,</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">τ</csymbol>
          <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">)</ci>
        </cerror>
        <cerror id="p1.1.m1.1.46.cmml" xref="p1.1.m1.1.46">
          <csymbol cd="ambiguous" id="p1.1.m1.1.46a.cmml" xref="p1.1.m1.1.46">fragments</csymbol>
          <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">(</ci>
          <cn type="integer" id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">3</cn>
          <apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
            <ci id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">¯</ci>
            <ci id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">𝑟</ci>
          </apply>
          <apply id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
            <ci id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">´</ci>
            <csymbol cd="latexml" id="p1.1.m1.1.21.2.cmml" xref="p1.1.m1.1.21.2">absent</csymbol>
          </apply>
          <csymbol cd="latexml" id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">tensor-product</csymbol>
          <apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
            <ci id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">¯</ci>
            <ci id="p1.1.m1.1.23.2.cmml" xref="p1.1.m1.1.23.2">𝑟</ci>
          </apply>
          <apply id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">
            <ci id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">´</ci>
            <csymbol cd="latexml" id="p1.1.m1.1.24.2.cmml" xref="p1.1.m1.1.24.2">absent</csymbol>
          </apply>
          <minus id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25"/>
          <csymbol cd="unknown" id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">r</csymbol>
          <apply id="p1.1.m1.1.45.cmml" xref="p1.1.m1.1.45">
            <csymbol cd="ambiguous" id="p1.1.m1.1.45.1.cmml" xref="p1.1.m1.1.45">superscript</csymbol>
            <apply id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">
              <ci id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27.1">´</ci>
              <csymbol cd="latexml" id="p1.1.m1.1.27.2.cmml" xref="p1.1.m1.1.27.2">absent</csymbol>
            </apply>
            <cn type="integer" id="p1.1.m1.1.28.1.cmml" xref="p1.1.m1.1.28.1">2</cn>
          </apply>
          <apply id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">
            <ci id="p1.1.m1.1.29.1.cmml" xref="p1.1.m1.1.29.1">¯</ci>
            <apply id="p1.1.m1.1.29.2.cmml" xref="p1.1.m1.1.29.2">
              <ci id="p1.1.m1.1.29.2.1.1.cmml" xref="p1.1.m1.1.29.2.1.1">¯</ci>
              <cn type="integer" id="p1.1.m1.1.29.2.1.2.cmml" xref="p1.1.m1.1.29.2.1.2">1</cn>
            </apply>
          </apply>
          <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">)</ci>
        </cerror>
        <eq id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31"/>
        <ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">:</ci>
        <apply id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">
          <ci id="p1.1.m1.1.33.1.cmml" xref="p1.1.m1.1.33.1">~</ci>
          <apply id="p1.1.m1.1.33.2.cmml" xref="p1.1.m1.1.33.2">
            <ci id="p1.1.m1.1.33.2.1.1.cmml" xref="p1.1.m1.1.33.2.1.1">¯</ci>
            <apply id="p1.1.m1.1.33.2.1.2.cmml" xref="p1.1.m1.1.33.2.1.2">
              <ci id="p1.1.m1.1.33.2.1.2.1.1.cmml" xref="p1.1.m1.1.33.2.1.2.1.1">¯</ci>
              <ci id="p1.1.m1.1.33.2.1.2.1.2.cmml" xref="p1.1.m1.1.33.2.1.2.1.2">𝑄</ci>
            </apply>
          </apply>
        </apply>
        <minus id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34"/>
        <apply id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">
          <divide id="p1.1.m1.1.35.1.cmml" xref="p1.1.m1.1.35"/>
          <cn type="integer" id="p1.1.m1.1.35.2.cmml" xref="p1.1.m1.1.35.2">1</cn>
          <cn type="integer" id="p1.1.m1.1.35.3.cmml" xref="p1.1.m1.1.35.3">3</cn>
        </apply>
        <cerror id="p1.1.m1.1.48.cmml" xref="p1.1.m1.1.48">
          <csymbol cd="ambiguous" id="p1.1.m1.1.48a.cmml" xref="p1.1.m1.1.48">fragments</csymbol>
          <ci id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37">t</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38">r</csymbol>
          <cerror id="p1.1.m1.1.47.cmml" xref="p1.1.m1.1.47">
            <csymbol cd="ambiguous" id="p1.1.m1.1.47a.cmml" xref="p1.1.m1.1.47">fragments</csymbol>
            <ci id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">(</ci>
            <apply id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40">
              <ci id="p1.1.m1.1.40.1.cmml" xref="p1.1.m1.1.40.1">~</ci>
              <apply id="p1.1.m1.1.40.2.cmml" xref="p1.1.m1.1.40.2">
                <ci id="p1.1.m1.1.40.2.1.1.cmml" xref="p1.1.m1.1.40.2.1.1">¯</ci>
                <apply id="p1.1.m1.1.40.2.1.2.cmml" xref="p1.1.m1.1.40.2.1.2">
                  <ci id="p1.1.m1.1.40.2.1.2.1.1.cmml" xref="p1.1.m1.1.40.2.1.2.1.1">¯</ci>
                  <ci id="p1.1.m1.1.40.2.1.2.1.2.cmml" xref="p1.1.m1.1.40.2.1.2.1.2">𝑄</ci>
                </apply>
              </apply>
            </apply>
            <ci id="p1.1.m1.1.41.cmml" xref="p1.1.m1.1.41">)</ci>
          </cerror>
          <ci id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42">)</ci>
        </cerror>
        <apply id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43">
          <ci id="p1.1.m1.1.43.1.cmml" xref="p1.1.m1.1.43.1">¯</ci>
          <apply id="p1.1.m1.1.43.2.cmml" xref="p1.1.m1.1.43.2">
            <ci id="p1.1.m1.1.43.2.1.1.cmml" xref="p1.1.m1.1.43.2.1.1">¯</ci>
            <cn type="integer" id="p1.1.m1.1.43.2.1.2.cmml" xref="p1.1.m1.1.43.2.1.2">1</cn>
          </apply>
        </apply>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\bar{\bar{Q}}\left(\tau\right)=\int{{{d}^{3}}r%
\acute{\ }\rho\left(\bar{r}\acute{\ },\tau\right)}\left(3\bar{r}\acute{\ }%
\otimes\bar{r}\acute{\ }-r{{\acute{\ }}^{2}}\bar{\bar{1}}\right)=:\tilde{\bar{%
\bar{Q}}}-\frac{1}{3}\left(tr\left({\tilde{\bar{\bar{Q}}}}\right)\right)\bar{%
\bar{1}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (3.659 KB / 467 B) :

Q¯¯(τ)=∫d3r´ρ(r¯´,τ)(3r¯´⊗r¯´−r´21¯¯)=:Q¯¯~−13(tr(Q¯¯~))1¯¯
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>Q</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03C4;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mi>&#x03C1;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>,</mo><mi>&#x03C4;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>3</mn><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>&#x2297;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>&#x2212;</mo><mi>r</mi><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mn>1</mn><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>:</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>Q</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mi>r</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>Q</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mn>1</mn><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Multipolstrahlung page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“