General
Display information for equation id:math.63486.21 on revision:63486
* Page found: Results of Integrals with Coalescing Saddles (eq math.63486.21)
(force rerendering)Cannot find the equation data in the database. Fetching from revision text.
Occurrences on the following pages:
Hash: cb22c6e013e68135f2fa0666c25bcdfb
TeX (original user input):
\theta_{-}(\phi) = \tfrac{1}{2}(\pi-\phi-\asin@{3\sin@@{\phi}})
TeX (checked):
LaTeXML (experimental; uses MathML) rendering
MathML (5.448 KB / 1.042 KB) :

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\theta_{-}(\phi)=\tfrac{1}{2}(\pi-\phi-% \operatorname{arcsin}\left(3\sin\phi\right))}}" display="inline">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
<mrow id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
<msub id="p1.1.m1.1.15.1.2" xref="p1.1.m1.1.15.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">θ</mi>
<mo id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">-</mo>
</msub>
<mo id="p1.1.m1.1.15.1.1" xref="p1.1.m1.1.15.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.15.1.3" xref="p1.1.m1.1.15.1.cmml">
<mo stretchy="false" id="p1.1.m1.1.3" xref="p1.1.m1.1.15.1.cmml">(</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">ϕ</mi>
<mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.15.1.cmml">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mrow id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">
<mfrac id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
<mn id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">1</mn>
<mn id="p1.1.m1.1.7.3" xref="p1.1.m1.1.7.3.cmml">2</mn>
</mfrac>
<mo id="p1.1.m1.1.15.2.1" xref="p1.1.m1.1.15.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.15.2.2" xref="p1.1.m1.1.15.2.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.15.2.2.2.cmml">(</mo>
<mrow id="p1.1.m1.1.15.2.2.2" xref="p1.1.m1.1.15.2.2.2.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">π</mi>
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">-</mo>
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">ϕ</mi>
<mo id="p1.1.m1.1.10a" xref="p1.1.m1.1.10.cmml">-</mo>
<mrow id="p1.1.m1.1.13.7.2" xref="p1.1.m1.1.13.1.cmml">
<mi id="p1.1.m1.1.13.2.1.7" xref="p1.1.m1.1.13.2.1.1.cmml">arcsin</mi>
<mo id="p1.1.m1.1.13.7.2a" xref="p1.1.m1.1.13.1.cmml"></mo>
<mrow id="p1.1.m1.1.13.7.2.1" xref="p1.1.m1.1.13.1.cmml">
<mo id="p1.1.m1.1.13.4" xref="p1.1.m1.1.13.1.cmml">(</mo>
<mrow id="p1.1.m1.1.13.5" xref="p1.1.m1.1.13.5.cmml">
<mn id="p1.1.m1.1.13.5.1" xref="p1.1.m1.1.13.5.1.cmml">3</mn>
<mo id="p1.1.m1.1.13.5.3" xref="p1.1.m1.1.13.5.3.cmml"></mo>
<mrow id="p1.1.m1.1.13.5.2.5" xref="p1.1.m1.1.13.5.2.1.cmml">
<mi id="p1.1.m1.1.13.5.2.2.1.2" xref="p1.1.m1.1.13.5.2.2.1.1.cmml">sin</mi>
<mo id="p1.1.m1.1.13.5.2.5a" xref="p1.1.m1.1.13.5.2.1.cmml"></mo>
<mi id="p1.1.m1.1.13.5.2.4" xref="p1.1.m1.1.13.5.2.4.cmml">ϕ</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.13.6" xref="p1.1.m1.1.13.1.cmml">)</mo>
</mrow>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.15.2.2.2.cmml">)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
<times id="p1.1.m1.1.15.1.1.cmml" xref="p1.1.m1.1.15.1.1"/>
<apply id="p1.1.m1.1.15.1.2.cmml" xref="p1.1.m1.1.15.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.15.1.2.1.cmml" xref="p1.1.m1.1.15.1.2">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝜃</ci>
<minus id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1"/>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">italic-ϕ</ci>
</apply>
<apply id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">
<times id="p1.1.m1.1.15.2.1.cmml" xref="p1.1.m1.1.15.2.1"/>
<apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
<divide id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7"/>
<cn type="integer" id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">1</cn>
<cn type="integer" id="p1.1.m1.1.7.3.cmml" xref="p1.1.m1.1.7.3">2</cn>
</apply>
<apply id="p1.1.m1.1.15.2.2.2.cmml" xref="p1.1.m1.1.15.2.2">
<minus id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝜋</ci>
<ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">italic-ϕ</ci>
<apply id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.7.2">
<arcsin id="p1.1.m1.1.13.2.1.1.cmml" xref="p1.1.m1.1.13.2.1.7"/>
<apply id="p1.1.m1.1.13.5.cmml" xref="p1.1.m1.1.13.5">
<times id="p1.1.m1.1.13.5.3.cmml" xref="p1.1.m1.1.13.5.3"/>
<cn type="integer" id="p1.1.m1.1.13.5.1.cmml" xref="p1.1.m1.1.13.5.1">3</cn>
<apply id="p1.1.m1.1.13.5.2.1.cmml" xref="p1.1.m1.1.13.5.2.5">
<sin id="p1.1.m1.1.13.5.2.2.1.1.cmml" xref="p1.1.m1.1.13.5.2.2.1.2"/>
<ci id="p1.1.m1.1.13.5.2.4.cmml" xref="p1.1.m1.1.13.5.2.4">italic-ϕ</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\theta_{-}(\phi)=\tfrac{1}{2}(\pi-\phi-%
\operatorname{arcsin}\left(3\sin\phi\right))}}</annotation>
</semantics>
</math>
SVG (11.875 KB / 4.383 KB) :
SVG with PNG fallback (MathML can be enabled via browser plugin) rendering
Failed to get svg.PNG (0 B / 8 B) :
Failed getting PNG[5fea4b2db41119f61aabcd31] /index.php?title=Special:FormulaInfo&pid=63486&eid=math.63486.21 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 Integrals with Coalescing Saddles page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results