General
Display information for equation id:math.63478.17 on revision:63478
* Page found: Results of Functions of Number Theory (eq math.63478.17)
(force rerendering)Cannot find the equation data in the database. Fetching from revision text.
Occurrences on the following pages:
Hash: 086ae81845412098e701a2b21d015ec1
TeX (original user input):
\EulerPhi@{x} = \prod_{m=1}^{\infty}(1-x^{m})
TeX (checked):
LaTeXML (experimental; uses MathML) rendering
MathML (4.47 KB / 978 B) :

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\mathit{f}\left(x\right)=\prod_{m=1}^{\infty}(1-x^% {m})}}" display="inline">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
<mrow id="p1.1.m1.1.1.7.2" xref="p1.1.m1.1.1.1.cmml">
<mi id="p1.1.m1.1.1.2.1.2" xref="p1.1.m1.1.1.2.1.1.cmml">f</mi>
<mo id="p1.1.m1.1.1.7.2a" xref="p1.1.m1.1.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.1.7.2.1" xref="p1.1.m1.1.1.1.cmml">
<mo id="p1.1.m1.1.1.4" xref="p1.1.m1.1.1.1.cmml">(</mo>
<mi id="p1.1.m1.1.1.5" xref="p1.1.m1.1.1.5.cmml">x</mi>
<mo id="p1.1.m1.1.1.6" xref="p1.1.m1.1.1.1.cmml">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.12.1.1.cmml">
<munderover id="p1.1.m1.1.12.1.1a" xref="p1.1.m1.1.12.1.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">∏</mo>
<mrow id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">
<mi id="p1.1.m1.1.4.1.1" xref="p1.1.m1.1.4.1.1.cmml">m</mi>
<mo id="p1.1.m1.1.4.1.2" xref="p1.1.m1.1.4.1.2.cmml">=</mo>
<mn id="p1.1.m1.1.4.1.3" xref="p1.1.m1.1.4.1.3.cmml">1</mn>
</mrow>
<mi mathvariant="normal" id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">∞</mi>
</munderover>
</mstyle>
<mrow id="p1.1.m1.1.12.1.2" xref="p1.1.m1.1.12.1.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.12.1.2.2.cmml">(</mo>
<mrow id="p1.1.m1.1.12.1.2.2" xref="p1.1.m1.1.12.1.2.2.cmml">
<mn id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">1</mn>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">-</mo>
<msup id="p1.1.m1.1.12.1.2.2.1" xref="p1.1.m1.1.12.1.2.2.1.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">x</mi>
<mi id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">m</mi>
</msup>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.12.1.2.2.cmml">)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<apply id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.7.2">
<csymbol cd="dlmf" id="p1.1.m1.1.1.2.1.1.cmml" xref="p1.1.m1.1.1.2.1.2">Euler-phi</csymbol>
<ci id="p1.1.m1.1.1.5.cmml" xref="p1.1.m1.1.1.5">𝑥</ci>
</apply>
<apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
<apply id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.12.1.1.1.cmml" xref="p1.1.m1.1.12.1.1">superscript</csymbol>
<apply id="p1.1.m1.1.12.1.1.2.cmml" xref="p1.1.m1.1.12.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.12.1.1.2.1.cmml" xref="p1.1.m1.1.12.1.1">subscript</csymbol>
<csymbol cd="latexml" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">product</csymbol>
<apply id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">
<eq id="p1.1.m1.1.4.1.2.cmml" xref="p1.1.m1.1.4.1.2"/>
<ci id="p1.1.m1.1.4.1.1.cmml" xref="p1.1.m1.1.4.1.1">𝑚</ci>
<cn type="integer" id="p1.1.m1.1.4.1.3.cmml" xref="p1.1.m1.1.4.1.3">1</cn>
</apply>
</apply>
<infinity id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1"/>
</apply>
<apply id="p1.1.m1.1.12.1.2.2.cmml" xref="p1.1.m1.1.12.1.2">
<minus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<cn type="integer" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">1</cn>
<apply id="p1.1.m1.1.12.1.2.2.1.cmml" xref="p1.1.m1.1.12.1.2.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.12.1.2.2.1.1.cmml" xref="p1.1.m1.1.12.1.2.2.1">superscript</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑥</ci>
<ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">𝑚</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\mathit{f}\left(x\right)=\prod_{m=1}^{\infty}(1-x^%
{m})}}</annotation>
</semantics>
</math>
SVG (7.661 KB / 2.837 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[a1607b35efccdaca38734d32] /index.php?title=Special:FormulaInfo&pid=63478&eid=math.63478.17 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 Functions of Number Theory page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results