Jump to navigation Jump to search

General

Display information for equation id:math.2141.16 on revision:2141

* Page found: Polarisation (eq math.2141.16)

(force rerendering)

Occurrences on the following pages:

Hash: 5864f231da5f644fd88c32208dd0696b

TeX (original user input): 

\int_{V}^{{}}{{{d}^{3}}r{{{\bar{P}}}_{m}}\left( \bar{r},t \right)=\sum\limits_{i}{{}}{{{\bar{p}}}_{i}}}

LaTeXML (experimental; uses MathML) rendering

MathML (6.488 KB / 1.19 KB) :

∫ V d 3 ⁢ r ⁢ P ¯ m ⁢ ( r ¯ , t ) = ∑ i p ¯ i subscript 𝑉 superscript 𝑑 3 𝑟 subscript ¯ 𝑃 𝑚 ¯ 𝑟 𝑡 subscript 𝑖 subscript ¯ 𝑝 𝑖 {\displaystyle{\displaystyle\int_{V}{{{d}^{3}}r{{{\bar{P}}}_{m}}\left(\bar{r},% t\right)=\sum\limits_{i}{{}}{{{\bar{p}}}_{i}}}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\int_{V}{{{d}^{3}}r{{{\bar{P}}}_{m}}\left(\bar{r},%&#10;t\right)=\sum\limits_{i}{{}}{{{\bar{p}}}_{i}}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
      <mrow id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.18.1.1" xref="p1.1.m1.1.18.1.1.cmml">
          <msub id="p1.1.m1.1.18.1.1a" xref="p1.1.m1.1.18.1.1.cmml">
            <mo largeop="true" symmetric="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">∫</mo>
            <mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">V</mi>
          </msub>
        </mstyle>
        <mrow id="p1.1.m1.1.18.1.2" xref="p1.1.m1.1.18.1.2.cmml">
          <msup id="p1.1.m1.1.18.1.2.2" xref="p1.1.m1.1.18.1.2.2.cmml">
            <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">d</mi>
            <mn id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">3</mn>
          </msup>
          <mo id="p1.1.m1.1.18.1.2.1" xref="p1.1.m1.1.18.1.2.1.cmml">⁢</mo>
          <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">r</mi>
          <mo id="p1.1.m1.1.18.1.2.1a" xref="p1.1.m1.1.18.1.2.1.cmml">⁢</mo>
          <msub id="p1.1.m1.1.18.1.2.3" xref="p1.1.m1.1.18.1.2.3.cmml">
            <mover accent="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
              <mi id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">P</mi>
              <mo stretchy="false" id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">¯</mo>
            </mover>
            <mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">m</mi>
          </msub>
          <mo id="p1.1.m1.1.18.1.2.1b" xref="p1.1.m1.1.18.1.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.18.1.2.4" xref="p1.1.m1.1.18.1.2.4.1.cmml">
            <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.18.1.2.4.1.cmml">(</mo>
            <mover accent="true" id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
              <mi id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">r</mi>
              <mo stretchy="false" id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">¯</mo>
            </mover>
            <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.18.1.2.4.1.cmml">,</mo>
            <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">t</mi>
            <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.18.1.2.4.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">=</mo>
      <mrow id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.18.2.1" xref="p1.1.m1.1.18.2.1.cmml">
          <munder id="p1.1.m1.1.18.2.1a" xref="p1.1.m1.1.18.2.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">∑</mo>
            <mi id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">i</mi>
          </munder>
        </mstyle>
        <msub id="p1.1.m1.1.18.2.2" xref="p1.1.m1.1.18.2.2.cmml">
          <mover accent="true" id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">
            <mi id="p1.1.m1.1.16.2" xref="p1.1.m1.1.16.2.cmml">p</mi>
            <mo stretchy="false" id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">¯</mo>
          </mover>
          <mi id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">i</mi>
        </msub>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
        <eq id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
        <apply id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">
          <apply id="p1.1.m1.1.18.1.1.cmml" xref="p1.1.m1.1.18.1.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.18.1.1.1.cmml" xref="p1.1.m1.1.18.1.1">subscript</csymbol>
            <int id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
            <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝑉</ci>
          </apply>
          <apply id="p1.1.m1.1.18.1.2.cmml" xref="p1.1.m1.1.18.1.2">
            <times id="p1.1.m1.1.18.1.2.1.cmml" xref="p1.1.m1.1.18.1.2.1"/>
            <apply id="p1.1.m1.1.18.1.2.2.cmml" xref="p1.1.m1.1.18.1.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.18.1.2.2.1.cmml" xref="p1.1.m1.1.18.1.2.2">superscript</csymbol>
              <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑑</ci>
              <cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">3</cn>
            </apply>
            <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑟</ci>
            <apply id="p1.1.m1.1.18.1.2.3.cmml" xref="p1.1.m1.1.18.1.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.18.1.2.3.1.cmml" xref="p1.1.m1.1.18.1.2.3">subscript</csymbol>
              <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
                <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">¯</ci>
                <ci id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">𝑃</ci>
              </apply>
              <ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">𝑚</ci>
            </apply>
            <interval closure="open" id="p1.1.m1.1.18.1.2.4.1.cmml" xref="p1.1.m1.1.18.1.2.4">
              <apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
                <ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">¯</ci>
                <ci id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">𝑟</ci>
              </apply>
              <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝑡</ci>
            </interval>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">
          <apply id="p1.1.m1.1.18.2.1.cmml" xref="p1.1.m1.1.18.2.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.18.2.1.1.cmml" xref="p1.1.m1.1.18.2.1">subscript</csymbol>
            <sum id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
            <ci id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">𝑖</ci>
          </apply>
          <apply id="p1.1.m1.1.18.2.2.cmml" xref="p1.1.m1.1.18.2.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.18.2.2.1.cmml" xref="p1.1.m1.1.18.2.2">subscript</csymbol>
            <apply id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">
              <ci id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">¯</ci>
              <ci id="p1.1.m1.1.16.2.cmml" xref="p1.1.m1.1.16.2">𝑝</ci>
            </apply>
            <ci id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">𝑖</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\int_{V}{{{d}^{3}}r{{{\bar{P}}}_{m}}\left(\bar{r},%
t\right)=\sum\limits_{i}{{}}{{{\bar{p}}}_{i}}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML can be enabled via browser plugin) rendering

MathML (2.726 KB / 572 B) :

∫ V d 3 r P ¯ m ( r ¯ , t ) = ∑ i p ¯ i {\displaystyle \int _{V}^{}{{{d}^{3}}r{{\bar {P}}_{m}}\left({\bar {r}},t\right)=\sum \limits _{i}{}{{\bar {p}}_{i}}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \int _{V}^{}{{{d}^{3}}r{{\bar {P}}_{m}}\left({\bar {r}},t\right)=\sum \limits _{i}{}{{\bar {p}}_{i}}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msubsup>
          <mo>&#x222B;<!-- ∫ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>V</mi>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">

          </mrow>
        </msubsup>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <msup>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>d</mi>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mn>3</mn>
              </mrow>
            </msup>
          </mrow>
          <mi>r</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <msub>
              <mrow class="MJX-TeXAtom-ORD">
                <mrow class="MJX-TeXAtom-ORD">
                  <mover>
                    <mi>P</mi>
                    <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
                  </mover>
                </mrow>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>m</mi>
              </mrow>
            </msub>
          </mrow>
          <mrow>
            <mo>(</mo>
            <mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mrow class="MJX-TeXAtom-ORD">
                  <mover>
                    <mi>r</mi>
                    <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
                  </mover>
                </mrow>
              </mrow>
              <mo>,</mo>
              <mi>t</mi>
            </mrow>
            <mo>)</mo>
          </mrow>
          <mo>=</mo>
          <munder>
            <mo movablelimits="false">&#x2211;<!-- ∑ --></mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mi>i</mi>
            </mrow>
          </munder>
          <mrow class="MJX-TeXAtom-ORD">

          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <msub>
              <mrow class="MJX-TeXAtom-ORD">
                <mrow class="MJX-TeXAtom-ORD">
                  <mover>
                    <mi>p</mi>
                    <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
                  </mover>
                </mrow>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>i</mi>
              </mrow>
            </msub>
          </mrow>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \int _{V}^{}{{{d}^{3}}r{{\bar {P}}_{m}}\left({\bar {r}},t\right)=\sum \limits _{i}{}{{\bar {p}}_{i}}}}</annotation>
  </semantics>
</math>

SVG (10.094 KB / 4.352 KB) :

{\displaystyle \int _{V}^{}{{{d}^{3}}r{{\bar {P}}_{m}}\left({\bar {r}},t\right)=\sum \limits _{i}{}{{\bar {p}}_{i}}}}

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 Polarisation page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "http://physikerwelt.de:8080/w/index.php?title=Special:FormulaInfo"