Jump to navigation Jump to search

General

Display information for equation id:math.63469.113 on revision:63469

* Page found: Results of Elliptic Integrals (eq math.63469.113)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: 842da00ada1625e3676c61b7631a9486

TeX (original user input): 

\frac{2}{\pi}\compellintEk@{k} <= \left(\frac{1+{k^{\prime}}^{2}}{2}\right)^{1/2}

TeX (checked):

LaTeXML (experimental; uses MathML) rendering

MathML (5.597 KB / 1.093 KB) :

2 π ⁢ E ⁡ ( k ) ≤ ( 1 + k ′ 2 2 ) 1 / 2 2 𝜋 complete-elliptic-integral-second-kind-E 𝑘 superscript 1 superscript superscript 𝑘 ′ 2 2 1 2 {\displaystyle{\displaystyle\frac{2}{\pi}E\left(k\right)<=\left(\frac{1+{k^{% \prime}}^{2}}{2}\right)^{1/2}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\frac{2}{\pi}E\left(k\right)&lt;=\left(\frac{1+{k^{%&#10;\prime}}^{2}}{2}\right)^{1/2}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
      <mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
          <mfrac id="p1.1.m1.1.1a" xref="p1.1.m1.1.1.cmml">
            <mn id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">2</mn>
            <mi id="p1.1.m1.1.1.3" xref="p1.1.m1.1.1.3.cmml">π</mi>
          </mfrac>
        </mstyle>
        <mo id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.2.7.2" xref="p1.1.m1.1.2.1.cmml">
          <mi id="p1.1.m1.1.2.2.1.2" xref="p1.1.m1.1.2.2.1.1.cmml">E</mi>
          <mo id="p1.1.m1.1.2.7.2a" xref="p1.1.m1.1.2.1.cmml">⁡</mo>
          <mrow id="p1.1.m1.1.2.7.2.1" xref="p1.1.m1.1.2.1.cmml">
            <mo id="p1.1.m1.1.2.4" xref="p1.1.m1.1.2.1.cmml">(</mo>
            <mi id="p1.1.m1.1.2.5" xref="p1.1.m1.1.2.5.cmml">k</mi>
            <mo id="p1.1.m1.1.2.6" xref="p1.1.m1.1.2.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">≤</mo>
      <msup id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
        <mrow id="p1.1.m1.1.9.2.2" xref="p1.1.m1.1.6.cmml">
          <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.6.cmml">(</mo>
          <mstyle displaystyle="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
            <mfrac id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">
              <mrow id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
                <mn id="p1.1.m1.1.6.2.1" xref="p1.1.m1.1.6.2.1.cmml">1</mn>
                <mo id="p1.1.m1.1.6.2.2" xref="p1.1.m1.1.6.2.2.cmml">+</mo>
                <mmultiscripts id="p1.1.m1.1.6.2.6" xref="p1.1.m1.1.6.2.6.cmml">
                  <mi id="p1.1.m1.1.6.2.3" xref="p1.1.m1.1.6.2.3.cmml">k</mi>
                  <none id="p1.1.m1.1.6.2.6a" xref="p1.1.m1.1.6.2.6.cmml"/>
                  <mo id="p1.1.m1.1.6.2.4.1" xref="p1.1.m1.1.6.2.4.1.cmml">′</mo>
                  <none id="p1.1.m1.1.6.2.6b" xref="p1.1.m1.1.6.2.6.cmml"/>
                  <mn id="p1.1.m1.1.6.2.5.1" xref="p1.1.m1.1.6.2.5.1.cmml">2</mn>
                </mmultiscripts>
              </mrow>
              <mn id="p1.1.m1.1.6.3" xref="p1.1.m1.1.6.3.cmml">2</mn>
            </mfrac>
          </mstyle>
          <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.6.cmml">)</mo>
        </mrow>
        <mrow id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">
          <mn id="p1.1.m1.1.8.1.1" xref="p1.1.m1.1.8.1.1.cmml">1</mn>
          <mo id="p1.1.m1.1.8.1.2" xref="p1.1.m1.1.8.1.2.cmml">/</mo>
          <mn id="p1.1.m1.1.8.1.3" xref="p1.1.m1.1.8.1.3.cmml">2</mn>
        </mrow>
      </msup>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
        <leq id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
        <apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
          <times id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1"/>
          <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
            <divide id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1"/>
            <cn type="integer" id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">2</cn>
            <ci id="p1.1.m1.1.1.3.cmml" xref="p1.1.m1.1.1.3">𝜋</ci>
          </apply>
          <apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.7.2">
            <csymbol cd="dlmf" id="p1.1.m1.1.2.2.1.1.cmml" xref="p1.1.m1.1.2.2.1.2">complete-elliptic-integral-second-kind-E</csymbol>
            <ci id="p1.1.m1.1.2.5.cmml" xref="p1.1.m1.1.2.5">𝑘</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
          <csymbol cd="ambiguous" id="p1.1.m1.1.9.2.1.cmml" xref="p1.1.m1.1.9.2">superscript</csymbol>
          <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.9.2.2">
            <divide id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.9.2.2"/>
            <apply id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
              <plus id="p1.1.m1.1.6.2.2.cmml" xref="p1.1.m1.1.6.2.2"/>
              <cn type="integer" id="p1.1.m1.1.6.2.1.cmml" xref="p1.1.m1.1.6.2.1">1</cn>
              <apply id="p1.1.m1.1.6.2.6.cmml" xref="p1.1.m1.1.6.2.6">
                <csymbol cd="ambiguous" id="p1.1.m1.1.6.2.6.1.cmml" xref="p1.1.m1.1.6.2.6">superscript</csymbol>
                <apply id="p1.1.m1.1.6.2.6.2.cmml" xref="p1.1.m1.1.6.2.6">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.6.2.6.2.1.cmml" xref="p1.1.m1.1.6.2.6">superscript</csymbol>
                  <ci id="p1.1.m1.1.6.2.3.cmml" xref="p1.1.m1.1.6.2.3">𝑘</ci>
                  <ci id="p1.1.m1.1.6.2.4.1.cmml" xref="p1.1.m1.1.6.2.4.1">′</ci>
                </apply>
                <cn type="integer" id="p1.1.m1.1.6.2.5.1.cmml" xref="p1.1.m1.1.6.2.5.1">2</cn>
              </apply>
            </apply>
            <cn type="integer" id="p1.1.m1.1.6.3.cmml" xref="p1.1.m1.1.6.3">2</cn>
          </apply>
          <apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">
            <divide id="p1.1.m1.1.8.1.2.cmml" xref="p1.1.m1.1.8.1.2"/>
            <cn type="integer" id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.1.1">1</cn>
            <cn type="integer" id="p1.1.m1.1.8.1.3.cmml" xref="p1.1.m1.1.8.1.3">2</cn>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\frac{2}{\pi}E\left(k\right)&lt;=\left(\frac{1+{k^{%
\prime}}^{2}}{2}\right)^{1/2}}}</annotation>
  </semantics>
</math>

SVG (9.164 KB / 3.364 KB) :

{\displaystyle{\displaystyle\frac{2}{\pi}E\left(k\right)<=\left(\frac{1+{k^{% \prime}}^{2}}{2}\right)^{1/2}}}

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (0 B / 8 B) :

Failed to get svg.

PNG (0 B / 8 B) :

Failed getting PNG

[6ad6ee20ec097eb7c5247f37] /index.php?title=Special:FormulaInfo&pid=63469&eid=math.63469.113 MWException: TeX input is invalid.

Backtrace:

from /var/www/html/extensions/Math/src/MathRestbaseInterface.php(125)
#0 /var/www/html/extensions/Math/src/MathRestbaseInterface.php(418): MediaWiki\Extension\Math\MathRestbaseInterface->calculateHash()
#1 /var/www/html/extensions/Math/src/MathRestbaseInterface.php(116): MediaWiki\Extension\Math\MathRestbaseInterface->getContentRequest(string)
#2 /var/www/html/extensions/Math/src/MathRestbaseInterface.php(250): MediaWiki\Extension\Math\MathRestbaseInterface->getContent(string)
#3 /var/www/html/extensions/Math/src/MathRenderer.php(655): MediaWiki\Extension\Math\MathRestbaseInterface->getSvg()
#4 /var/www/html/extensions/Math/src/MathMathML.php(377): MediaWiki\Extension\Math\MathRenderer->getSvg()
#5 /var/www/html/extensions/Math/src/MathMathML.php(418): MediaWiki\Extension\Math\MathMathML->correctSvgStyle(NULL)
#6 /var/www/html/extensions/Math/src/MathMathML.php(500): MediaWiki\Extension\Math\MathMathML->getFallbackImage()
#7 /var/www/html/extensions/MathSearch/includes/FormulaInfo.php(302): MediaWiki\Extension\Math\MathMathML->getHtmlOutput()
#8 /var/www/html/extensions/MathSearch/includes/FormulaInfo.php(166): FormulaInfo->DisplayRendering(string, string)
#9 /var/www/html/extensions/MathSearch/includes/FormulaInfo.php(45): FormulaInfo->DisplayInfo(string, string)
#10 /var/www/html/includes/specialpage/SpecialPage.php(690): FormulaInfo->execute(NULL)
#11 /var/www/html/includes/specialpage/SpecialPageFactory.php(1423): SpecialPage->run(NULL)
#12 /var/www/html/includes/MediaWiki.php(316): MediaWiki\SpecialPage\SpecialPageFactory->executePath(string, RequestContext)
#13 /var/www/html/includes/MediaWiki.php(911): MediaWiki->performRequest()
#14 /var/www/html/includes/MediaWiki.php(568): MediaWiki->main()
#15 /var/www/html/index.php(50): MediaWiki->run()
#16 /var/www/html/index.php(46): wfIndexMain()
#17 {main}


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 Results of Elliptic Integrals page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "https://drmf-beta.wmflabs.org/wiki/Special:FormulaInfo"