Jump to navigation Jump to search

General

Display information for equation id:math.1164.0 on revision:1164

* Page found: Stefan-Boltzmann Gesetz (eq math.1164.0)

(force rerendering)

Occurrences on the following pages:

Hash: 5cce4fcd5dffc8f3b407aba9542f8546

TeX (original user input): 

U(T):=\int_{-\infty}^{\infty} u(\nu,T) \, d\nu = \sigma T^4

TeX (checked): 

U(T):=\int _{-\infty }^{\infty }u(\nu ,T)\,d\nu =\sigma T^{4}

LaTeXML (experimental; uses MathML) rendering

MathML (6.306 KB / 1.213 KB) :

U ⁢ ( T ) := ∫ - ∞ ∞ u ⁢ ( ν , T ) ⁢ 𝑑 ν = σ ⁢ T 4 assign 𝑈 𝑇 superscript subscript 𝑢 𝜈 𝑇 differential-d 𝜈 𝜎 superscript 𝑇 4 {\displaystyle{\displaystyle U(T):=\int_{-\infty}^{\infty}u(\nu,T)\,d\nu=% \sigma T^{4}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle U(T):=\int_{-\infty}^{\infty}u(\nu,T)\,d\nu=%&#10;\sigma T^{4}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
      <mrow id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">U</mi>
        <mo id="p1.1.m1.1.23.2.1" xref="p1.1.m1.1.23.2.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.23.2.2" xref="p1.1.m1.1.23.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.23.2.cmml">(</mo>
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">T</mi>
          <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.23.2.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">:=</mo>
      <mrow id="p1.1.m1.1.23.3" xref="p1.1.m1.1.23.3.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.23.3.1" xref="p1.1.m1.1.23.3.1.cmml">
          <msubsup id="p1.1.m1.1.23.3.1a" xref="p1.1.m1.1.23.3.1.cmml">
            <mo largeop="true" symmetric="true" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">∫</mo>
            <mrow id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">
              <mo id="p1.1.m1.1.8.1.1" xref="p1.1.m1.1.8.1.1.cmml">-</mo>
              <mi mathvariant="normal" id="p1.1.m1.1.8.1.2" xref="p1.1.m1.1.8.1.2.cmml">∞</mi>
            </mrow>
            <mi mathvariant="normal" id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">∞</mi>
          </msubsup>
        </mstyle>
        <mrow id="p1.1.m1.1.23.3.2" xref="p1.1.m1.1.23.3.2.cmml">
          <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">u</mi>
          <mo id="p1.1.m1.1.23.3.2.1" xref="p1.1.m1.1.23.3.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.23.3.2.2" xref="p1.1.m1.1.23.3.2.2.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.23.3.2.2.1.cmml">(</mo>
            <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">ν</mi>
            <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.23.3.2.2.1.cmml">,</mo>
            <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">T</mi>
            <mo rspace="4.2pt" stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.23.3.2.2.1.cmml">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.23.3.2.1a" xref="p1.1.m1.1.23.3.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.23.3.2.3" xref="p1.1.m1.1.23.3.2.3.cmml">
            <mo rspace="0pt" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">𝑑</mo>
            <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">ν</mi>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">=</mo>
      <mrow id="p1.1.m1.1.23.4" xref="p1.1.m1.1.23.4.cmml">
        <mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">σ</mi>
        <mo id="p1.1.m1.1.23.4.1" xref="p1.1.m1.1.23.4.1.cmml">⁢</mo>
        <msup id="p1.1.m1.1.23.4.2" xref="p1.1.m1.1.23.4.2.cmml">
          <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">T</mi>
          <mn id="p1.1.m1.1.22.1" xref="p1.1.m1.1.22.1.cmml">4</mn>
        </msup>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
        <and id="p1.1.m1.1.23a.cmml" xref="p1.1.m1.1.23"/>
        <apply id="p1.1.m1.1.23b.cmml" xref="p1.1.m1.1.23">
          <csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">assign</csymbol>
          <apply id="p1.1.m1.1.23.2.cmml" xref="p1.1.m1.1.23.2">
            <times id="p1.1.m1.1.23.2.1.cmml" xref="p1.1.m1.1.23.2.1"/>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑈</ci>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑇</ci>
          </apply>
          <apply id="p1.1.m1.1.23.3.cmml" xref="p1.1.m1.1.23.3">
            <apply id="p1.1.m1.1.23.3.1.cmml" xref="p1.1.m1.1.23.3.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.3.1.1.cmml" xref="p1.1.m1.1.23.3.1">superscript</csymbol>
              <apply id="p1.1.m1.1.23.3.1.2.cmml" xref="p1.1.m1.1.23.3.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.23.3.1.2.1.cmml" xref="p1.1.m1.1.23.3.1">subscript</csymbol>
                <int id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
                <apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">
                  <minus id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.1.1"/>
                  <infinity id="p1.1.m1.1.8.1.2.cmml" xref="p1.1.m1.1.8.1.2"/>
                </apply>
              </apply>
              <infinity id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1"/>
            </apply>
            <apply id="p1.1.m1.1.23.3.2.cmml" xref="p1.1.m1.1.23.3.2">
              <times id="p1.1.m1.1.23.3.2.1.cmml" xref="p1.1.m1.1.23.3.2.1"/>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑢</ci>
              <interval closure="open" id="p1.1.m1.1.23.3.2.2.1.cmml" xref="p1.1.m1.1.23.3.2.2">
                <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝜈</ci>
                <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑇</ci>
              </interval>
              <apply id="p1.1.m1.1.23.3.2.3.cmml" xref="p1.1.m1.1.23.3.2.3">
                <csymbol cd="latexml" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">differential-d</csymbol>
                <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝜈</ci>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.23c.cmml" xref="p1.1.m1.1.23">
          <eq id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
          <share href="#p1.1.m1.1.23.3.cmml" id="p1.1.m1.1.23d.cmml" xref="p1.1.m1.1.23"/>
          <apply id="p1.1.m1.1.23.4.cmml" xref="p1.1.m1.1.23.4">
            <times id="p1.1.m1.1.23.4.1.cmml" xref="p1.1.m1.1.23.4.1"/>
            <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">𝜎</ci>
            <apply id="p1.1.m1.1.23.4.2.cmml" xref="p1.1.m1.1.23.4.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.4.2.1.cmml" xref="p1.1.m1.1.23.4.2">superscript</csymbol>
              <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">𝑇</ci>
              <cn type="integer" id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22.1">4</cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle U(T):=\int_{-\infty}^{\infty}u(\nu,T)\,d\nu=%
\sigma T^{4}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML can be enabled via browser plugin) rendering

MathML (1.354 KB / 481 B) :

U ( T ) := ∫ − ∞ ∞ u ( ν , T ) d ν = σ T 4 {\displaystyle U(T):=\int _{-\infty }^{\infty }u(\nu ,T)\,d\nu =\sigma T^{4}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle U(T):=\int _{-\infty }^{\infty }u(\nu ,T)\,d\nu =\sigma T^{4}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>U</mi>
        <mo stretchy="false">(</mo>
        <mi>T</mi>
        <mo stretchy="false">)</mo>
        <mo>:=</mo>
        <msubsup>
          <mo>&#x222B;<!-- ∫ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mo>&#x2212;<!-- − --></mo>
            <mi mathvariant="normal">&#x221E;<!-- ∞ --></mi>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mi mathvariant="normal">&#x221E;<!-- ∞ --></mi>
          </mrow>
        </msubsup>
        <mi>u</mi>
        <mo stretchy="false">(</mo>
        <mi>&#x03BD;<!-- ν --></mi>
        <mo>,</mo>
        <mi>T</mi>
        <mo stretchy="false">)</mo>
        <mspace width="thinmathspace" />
        <mi>d</mi>
        <mi>&#x03BD;<!-- ν --></mi>
        <mo>=</mo>
        <mi>&#x03C3;<!-- σ --></mi>
        <msup>
          <mi>T</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>4</mn>
          </mrow>
        </msup>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle U(T):=\int _{-\infty }^{\infty }u(\nu ,T)\,d\nu =\sigma T^{4}}</annotation>
  </semantics>
</math>

SVG (8.248 KB / 3.523 KB) :

{\displaystyle U(T):=\int _{-\infty }^{\infty }u(\nu ,T)\,d\nu =\sigma T^{4}}

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 Stefan-Boltzmann Gesetz 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"