Jump to navigation Jump to search

General

Display information for equation id:math.63469.107 on revision:63469

* Page found: Results of Elliptic Integrals (eq math.63469.107)

(force rerendering)

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

Occurrences on the following pages:

Hash: f790b7b643c7e36e43e5523b3d9613a5

TeX (original user input):

1 <= (2/\pi)\sqrt{1-\alpha^{2}}\compellintPik@{\alpha^{2}}{k}\leq 1/k^{\prime}

TeX (checked):

LaTeXML (experimental; uses MathML) rendering

MathML (6.305 KB / 1.207 KB) :

1 ( 2 / π ) 1 - α 2 Π ( α 2 , k ) 1 / k 1 2 𝜋 1 superscript 𝛼 2 complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 1 superscript 𝑘 {\displaystyle{\displaystyle 1<=(2/\pi)\sqrt{1-\alpha^{2}}\Pi\left(\alpha^{2},% k\right)\leq 1/k^{\prime}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle 1&lt;=(2/\pi)\sqrt{1-\alpha^{2}}\Pi\left(\alpha^{2},%&#10;k\right)\leq 1/k^{\prime}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">
      <mn id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">1</mn>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml"></mo>
      <mrow id="p1.1.m1.1.16.2" xref="p1.1.m1.1.16.2.cmml">
        <mrow id="p1.1.m1.1.16.2.2" xref="p1.1.m1.1.16.2.2.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.16.2.2.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.16.2.2.2" xref="p1.1.m1.1.16.2.2.2.cmml">
            <mn id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">2</mn>
            <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">/</mo>
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">π</mi>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.16.2.2.2.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.16.2.1" xref="p1.1.m1.1.16.2.1.cmml"></mo>
        <msqrt id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
          <mrow id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
            <mn id="p1.1.m1.1.9.2.1" xref="p1.1.m1.1.9.2.1.cmml">1</mn>
            <mo id="p1.1.m1.1.9.2.2" xref="p1.1.m1.1.9.2.2.cmml">-</mo>
            <msup id="p1.1.m1.1.9.2.5" xref="p1.1.m1.1.9.2.5.cmml">
              <mi id="p1.1.m1.1.9.2.3" xref="p1.1.m1.1.9.2.3.cmml">α</mi>
              <mn id="p1.1.m1.1.9.2.4.1" xref="p1.1.m1.1.9.2.4.1.cmml">2</mn>
            </msup>
          </mrow>
        </msqrt>
        <mo id="p1.1.m1.1.16.2.1a" xref="p1.1.m1.1.16.2.1.cmml"></mo>
        <mrow id="p1.1.m1.1.10.9.2" xref="p1.1.m1.1.10.1.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.10.2.1.2" xref="p1.1.m1.1.10.2.1.1.cmml">Π</mi>
          <mo id="p1.1.m1.1.10.9.2a" xref="p1.1.m1.1.10.1.cmml"></mo>
          <mrow id="p1.1.m1.1.10.9.2.1" xref="p1.1.m1.1.10.1.cmml">
            <mo id="p1.1.m1.1.10.4" xref="p1.1.m1.1.10.1.cmml">(</mo>
            <msup id="p1.1.m1.1.10.5" xref="p1.1.m1.1.10.5.cmml">
              <mi id="p1.1.m1.1.10.5.1" xref="p1.1.m1.1.10.5.1.cmml">α</mi>
              <mn id="p1.1.m1.1.10.5.2.1" xref="p1.1.m1.1.10.5.2.1.cmml">2</mn>
            </msup>
            <mo id="p1.1.m1.1.10.6" xref="p1.1.m1.1.10.1.cmml">,</mo>
            <mi id="p1.1.m1.1.10.7" xref="p1.1.m1.1.10.7.cmml">k</mi>
            <mo id="p1.1.m1.1.10.8" xref="p1.1.m1.1.10.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml"></mo>
      <mrow id="p1.1.m1.1.16.3" xref="p1.1.m1.1.16.3.cmml">
        <mn id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">1</mn>
        <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">/</mo>
        <msup id="p1.1.m1.1.16.3.1" xref="p1.1.m1.1.16.3.1.cmml">
          <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">k</mi>
          <mo id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml"></mo>
        </msup>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">
        <and id="p1.1.m1.1.16a.cmml" xref="p1.1.m1.1.16"/>
        <apply id="p1.1.m1.1.16b.cmml" xref="p1.1.m1.1.16">
          <leq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
          <cn type="integer" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">1</cn>
          <apply id="p1.1.m1.1.16.2.cmml" xref="p1.1.m1.1.16.2">
            <times id="p1.1.m1.1.16.2.1.cmml" xref="p1.1.m1.1.16.2.1"/>
            <apply id="p1.1.m1.1.16.2.2.2.cmml" xref="p1.1.m1.1.16.2.2">
              <divide id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
              <cn type="integer" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">2</cn>
              <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝜋</ci>
            </apply>
            <apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
              <root id="p1.1.m1.1.9a.cmml" xref="p1.1.m1.1.9"/>
              <apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
                <minus id="p1.1.m1.1.9.2.2.cmml" xref="p1.1.m1.1.9.2.2"/>
                <cn type="integer" id="p1.1.m1.1.9.2.1.cmml" xref="p1.1.m1.1.9.2.1">1</cn>
                <apply id="p1.1.m1.1.9.2.5.cmml" xref="p1.1.m1.1.9.2.5">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.9.2.5.1.cmml" xref="p1.1.m1.1.9.2.5">superscript</csymbol>
                  <ci id="p1.1.m1.1.9.2.3.cmml" xref="p1.1.m1.1.9.2.3">𝛼</ci>
                  <cn type="integer" id="p1.1.m1.1.9.2.4.1.cmml" xref="p1.1.m1.1.9.2.4.1">2</cn>
                </apply>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.9.2">
              <csymbol cd="dlmf" id="p1.1.m1.1.10.2.1.1.cmml" xref="p1.1.m1.1.10.2.1.2">complete-elliptic-integral-third-kind-Pi</csymbol>
              <apply id="p1.1.m1.1.10.5.cmml" xref="p1.1.m1.1.10.5">
                <csymbol cd="ambiguous" id="p1.1.m1.1.10.5.3.cmml" xref="p1.1.m1.1.10.5">superscript</csymbol>
                <ci id="p1.1.m1.1.10.5.1.cmml" xref="p1.1.m1.1.10.5.1">𝛼</ci>
                <cn type="integer" id="p1.1.m1.1.10.5.2.1.cmml" xref="p1.1.m1.1.10.5.2.1">2</cn>
              </apply>
              <ci id="p1.1.m1.1.10.7.cmml" xref="p1.1.m1.1.10.7">𝑘</ci>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.16c.cmml" xref="p1.1.m1.1.16">
          <leq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
          <share href="#p1.1.m1.1.16.2.cmml" id="p1.1.m1.1.16d.cmml" xref="p1.1.m1.1.16"/>
          <apply id="p1.1.m1.1.16.3.cmml" xref="p1.1.m1.1.16.3">
            <divide id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
            <cn type="integer" id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">1</cn>
            <apply id="p1.1.m1.1.16.3.1.cmml" xref="p1.1.m1.1.16.3.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.16.3.1.1.cmml" xref="p1.1.m1.1.16.3.1">superscript</csymbol>
              <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑘</ci>
              <ci id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1"></ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle 1&lt;=(2/\pi)\sqrt{1-\alpha^{2}}\Pi\left(\alpha^{2},%
k\right)\leq 1/k^{\prime}}}</annotation>
  </semantics>
</math>

SVG (9.936 KB / 3.505 KB) :

{\displaystyle{\displaystyle 1<=(2/\pi)\sqrt{1-\alpha^{2}}\Pi\left(\alpha^{2},% k\right)\leq 1/k^{\prime}}}

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

[ddd0bd453456daee2b6f2930] /index.php?title=Special:FormulaInfo&pid=63469&eid=math.63469.107 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