Jump to navigation Jump to search

General

Display information for equation id:math.3025.9 on revision:3025

* Page found: Formula:KLS:01.08:19 (eq math.3025.9)

(force rerendering)

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

Occurrences on the following pages:

Hash: 4ddc204689e8d4f9f2b2e3c2097265d4

TeX (original user input): 

{\displaystyle \qPochhammer{a}{q}{\infty}=\prod_{k=0}^{\infty}(1-aq^k)
=\qPochhammer{a}{q^2}{\infty}\qPochhammer{aq}{q^2}{\infty}}

TeX (checked):

LaTeXML (experimental; uses MathML) rendering

MathML (9.791 KB / 1.522 KB) :

\qPochhammer ⁢ a ⁢ q ⁢ ∞ = ∏ k = 0 ∞ ( 1 - a ⁢ q k ) = \qPochhammer ⁢ a ⁢ q 2 ⁢ ∞ ⁢ \qPochhammer ⁢ a ⁢ q ⁢ q 2 ⁢ ∞ \qPochhammer 𝑎 𝑞 superscript subscript product 𝑘 0 1 𝑎 superscript 𝑞 𝑘 \qPochhammer 𝑎 superscript 𝑞 2 \qPochhammer 𝑎 𝑞 superscript 𝑞 2 {\displaystyle{\displaystyle{\displaystyle\qPochhammer{a}{q}{\infty}=\prod_{k=% 0}^{\infty}(1-aq^{k})=\qPochhammer{a}{q^{2}}{\infty}\qPochhammer{aq}{q^{2}}{% \infty}}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{\displaystyle\qPochhammer{a}{q}{\infty}=\prod_{k=%&#10;0}^{\infty}(1-aq^{k})=\qPochhammer{a}{q^{2}}{\infty}\qPochhammer{aq}{q^{2}}{%&#10;\infty}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">
      <mrow id="p1.1.m1.1.28.2" xref="p1.1.m1.1.28.2.cmml">
        <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.1" xref="p1.1.m1.1.1b.cmml">
          <mtext id="p1.1.m1.1.1a" xref="p1.1.m1.1.1b.cmml">\qPochhammer</mtext>
        </merror>
        <mo id="p1.1.m1.1.28.2.1" xref="p1.1.m1.1.28.2.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">a</mi>
        <mo id="p1.1.m1.1.28.2.1a" xref="p1.1.m1.1.28.2.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">q</mi>
        <mo id="p1.1.m1.1.28.2.1b" xref="p1.1.m1.1.28.2.1.cmml">⁢</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">∞</mi>
      </mrow>
      <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
      <mrow id="p1.1.m1.1.28.3" xref="p1.1.m1.1.28.3.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.28.3.1" xref="p1.1.m1.1.28.3.1.cmml">
          <munderover id="p1.1.m1.1.28.3.1a" xref="p1.1.m1.1.28.3.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">∏</mo>
            <mrow id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">
              <mi id="p1.1.m1.1.7.1.1" xref="p1.1.m1.1.7.1.1.cmml">k</mi>
              <mo id="p1.1.m1.1.7.1.2" xref="p1.1.m1.1.7.1.2.cmml">=</mo>
              <mn id="p1.1.m1.1.7.1.3" xref="p1.1.m1.1.7.1.3.cmml">0</mn>
            </mrow>
            <mi mathvariant="normal" id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">∞</mi>
          </munderover>
        </mstyle>
        <mrow id="p1.1.m1.1.28.3.2" xref="p1.1.m1.1.28.3.2.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.28.3.2.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.28.3.2.2" xref="p1.1.m1.1.28.3.2.2.cmml">
            <mn id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">1</mn>
            <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">-</mo>
            <mrow id="p1.1.m1.1.28.3.2.2.1" xref="p1.1.m1.1.28.3.2.2.1.cmml">
              <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">a</mi>
              <mo id="p1.1.m1.1.28.3.2.2.1.1" xref="p1.1.m1.1.28.3.2.2.1.1.cmml">⁢</mo>
              <msup id="p1.1.m1.1.28.3.2.2.1.2" xref="p1.1.m1.1.28.3.2.2.1.2.cmml">
                <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">q</mi>
                <mi id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">k</mi>
              </msup>
            </mrow>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.28.3.2.2.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">=</mo>
      <mrow id="p1.1.m1.1.28.4" xref="p1.1.m1.1.28.4.cmml">
        <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.17" xref="p1.1.m1.1.17b.cmml">
          <mtext id="p1.1.m1.1.17a" xref="p1.1.m1.1.17b.cmml">\qPochhammer</mtext>
        </merror>
        <mo id="p1.1.m1.1.28.4.1" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">a</mi>
        <mo id="p1.1.m1.1.28.4.1a" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <msup id="p1.1.m1.1.28.4.2" xref="p1.1.m1.1.28.4.2.cmml">
          <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">q</mi>
          <mn id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">2</mn>
        </msup>
        <mo id="p1.1.m1.1.28.4.1b" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">∞</mi>
        <mo id="p1.1.m1.1.28.4.1c" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.22" xref="p1.1.m1.1.22b.cmml">
          <mtext id="p1.1.m1.1.22a" xref="p1.1.m1.1.22b.cmml">\qPochhammer</mtext>
        </merror>
        <mo id="p1.1.m1.1.28.4.1d" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">a</mi>
        <mo id="p1.1.m1.1.28.4.1e" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">q</mi>
        <mo id="p1.1.m1.1.28.4.1f" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <msup id="p1.1.m1.1.28.4.3" xref="p1.1.m1.1.28.4.3.cmml">
          <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">q</mi>
          <mn id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">2</mn>
        </msup>
        <mo id="p1.1.m1.1.28.4.1g" xref="p1.1.m1.1.28.4.1.cmml">⁢</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">∞</mi>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">
        <and id="p1.1.m1.1.28a.cmml" xref="p1.1.m1.1.28"/>
        <apply id="p1.1.m1.1.28b.cmml" xref="p1.1.m1.1.28">
          <eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
          <apply id="p1.1.m1.1.28.2.cmml" xref="p1.1.m1.1.28.2">
            <times id="p1.1.m1.1.28.2.1.cmml" xref="p1.1.m1.1.28.2.1"/>
            <ci id="p1.1.m1.1.1b.cmml" xref="p1.1.m1.1.1">
              <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
                <mtext id="p1.1.m1.1.1a.cmml" xref="p1.1.m1.1.1">\qPochhammer</mtext>
              </merror>
            </ci>
            <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝑎</ci>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑞</ci>
            <infinity id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
          </apply>
          <apply id="p1.1.m1.1.28.3.cmml" xref="p1.1.m1.1.28.3">
            <apply id="p1.1.m1.1.28.3.1.cmml" xref="p1.1.m1.1.28.3.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.28.3.1.1.cmml" xref="p1.1.m1.1.28.3.1">superscript</csymbol>
              <apply id="p1.1.m1.1.28.3.1.2.cmml" xref="p1.1.m1.1.28.3.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.28.3.1.2.1.cmml" xref="p1.1.m1.1.28.3.1">subscript</csymbol>
                <csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">product</csymbol>
                <apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
                  <eq id="p1.1.m1.1.7.1.2.cmml" xref="p1.1.m1.1.7.1.2"/>
                  <ci id="p1.1.m1.1.7.1.1.cmml" xref="p1.1.m1.1.7.1.1">𝑘</ci>
                  <cn type="integer" id="p1.1.m1.1.7.1.3.cmml" xref="p1.1.m1.1.7.1.3">0</cn>
                </apply>
              </apply>
              <infinity id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1"/>
            </apply>
            <apply id="p1.1.m1.1.28.3.2.2.cmml" xref="p1.1.m1.1.28.3.2">
              <minus id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
              <cn type="integer" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">1</cn>
              <apply id="p1.1.m1.1.28.3.2.2.1.cmml" xref="p1.1.m1.1.28.3.2.2.1">
                <times id="p1.1.m1.1.28.3.2.2.1.1.cmml" xref="p1.1.m1.1.28.3.2.2.1.1"/>
                <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑎</ci>
                <apply id="p1.1.m1.1.28.3.2.2.1.2.cmml" xref="p1.1.m1.1.28.3.2.2.1.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.28.3.2.2.1.2.1.cmml" xref="p1.1.m1.1.28.3.2.2.1.2">superscript</csymbol>
                  <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝑞</ci>
                  <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">𝑘</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.28c.cmml" xref="p1.1.m1.1.28">
          <eq id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
          <share href="#p1.1.m1.1.28.3.cmml" id="p1.1.m1.1.28d.cmml" xref="p1.1.m1.1.28"/>
          <apply id="p1.1.m1.1.28.4.cmml" xref="p1.1.m1.1.28.4">
            <times id="p1.1.m1.1.28.4.1.cmml" xref="p1.1.m1.1.28.4.1"/>
            <ci id="p1.1.m1.1.17b.cmml" xref="p1.1.m1.1.17">
              <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">
                <mtext id="p1.1.m1.1.17a.cmml" xref="p1.1.m1.1.17">\qPochhammer</mtext>
              </merror>
            </ci>
            <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝑎</ci>
            <apply id="p1.1.m1.1.28.4.2.cmml" xref="p1.1.m1.1.28.4.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.28.4.2.1.cmml" xref="p1.1.m1.1.28.4.2">superscript</csymbol>
              <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝑞</ci>
              <cn type="integer" id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">2</cn>
            </apply>
            <infinity id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
            <ci id="p1.1.m1.1.22b.cmml" xref="p1.1.m1.1.22">
              <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">
                <mtext id="p1.1.m1.1.22a.cmml" xref="p1.1.m1.1.22">\qPochhammer</mtext>
              </merror>
            </ci>
            <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">𝑎</ci>
            <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">𝑞</ci>
            <apply id="p1.1.m1.1.28.4.3.cmml" xref="p1.1.m1.1.28.4.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.28.4.3.1.cmml" xref="p1.1.m1.1.28.4.3">superscript</csymbol>
              <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">𝑞</ci>
              <cn type="integer" id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">2</cn>
            </apply>
            <infinity id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27"/>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle{\displaystyle\qPochhammer{a}{q}{\infty}=\prod_{k=%
0}^{\infty}(1-aq^{k})=\qPochhammer{a}{q^{2}}{\infty}\qPochhammer{aq}{q^{2}}{%
\infty}}}}</annotation>
  </semantics>
</math>

SVG (13.58 KB / 3.602 KB) :

{\displaystyle{\displaystyle{\displaystyle\qPochhammer{a}{q}{\infty}=\prod_{k=% 0}^{\infty}(1-aq^{k})=\qPochhammer{a}{q^{2}}{\infty}\qPochhammer{aq}{q^{2}}{% \infty}}}}

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

[56ee18d28831a65f56d74b91] /index.php?title=Special:FormulaInfo&pid=3025&eid=math.3025.9 MWException: TeX input is invalid.

Backtrace:

from /var/www/html/extensions/Math/src/MathRestbaseInterface.php(126)
#0 /var/www/html/extensions/Math/src/MathRestbaseInterface.php(419): MediaWiki\Extension\Math\MathRestbaseInterface->calculateHash()
#1 /var/www/html/extensions/Math/src/MathRestbaseInterface.php(117): MediaWiki\Extension\Math\MathRestbaseInterface->getContentRequest(string)
#2 /var/www/html/extensions/Math/src/MathRestbaseInterface.php(251): MediaWiki\Extension\Math\MathRestbaseInterface->getContent(string)
#3 /var/www/html/extensions/Math/src/MathRenderer.php(674): MediaWiki\Extension\Math\MathRestbaseInterface->getSvg()
#4 /var/www/html/extensions/Math/src/MathMathML.php(385): MediaWiki\Extension\Math\MathRenderer->getSvg()
#5 /var/www/html/extensions/Math/src/MathMathML.php(426): MediaWiki\Extension\Math\MathMathML->correctSvgStyle(NULL)
#6 /var/www/html/extensions/Math/src/MathMathML.php(508): 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(688): FormulaInfo->execute(NULL)
#11 /var/www/html/includes/specialpage/SpecialPageFactory.php(1418): SpecialPage->run(NULL)
#12 /var/www/html/includes/MediaWiki.php(316): MediaWiki\SpecialPage\SpecialPageFactory->executePath(string, RequestContext)
#13 /var/www/html/includes/MediaWiki.php(916): MediaWiki->performRequest()
#14 /var/www/html/includes/MediaWiki.php(570): 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 Formula:KLS:01.08:19 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"