Jump to navigation Jump to search

General

Display information for equation id:math.3121.0 on revision:3121

* Page found: Formula:KLS:01.13:04 (eq math.3121.0)

(force rerendering)

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

Occurrences on the following pages:

Hash: ff05d2672dfc503698d0b4278535ad38

TeX (original user input): 

{\displaystyle 
\index{q-Euler transformation formula@$q$-Euler transformation formula}\index{Transformation formula!q-Euler@$q$-Euler}
\HyperpFq{2}{1}@@{a,b}{c}{z}=(1-z)^{c-a-b}\,\HyperpFq{2}{1}@@{c-a,c-b}{c}{z}
}

TeX (checked):

LaTeXML (experimental; uses MathML) rendering

MathML (9.517 KB / 1.461 KB) :

\HyperpFq ⁢ 21 ⁢ @ ⁢ @ ⁢ a , b ⁢ c ⁢ z = ( 1 - z ) c - a - b ⁢ \HyperpFq ⁢ 21 ⁢ @ ⁢ @ ⁢ c - a , c - b ⁢ c ⁢ z formulae-sequence \HyperpFq 21 @ @ 𝑎 𝑏 𝑐 𝑧 superscript 1 𝑧 𝑐 𝑎 𝑏 \HyperpFq 21 @ @ 𝑐 𝑎 𝑐 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{\displaystyle{}{}\HyperpFq{2}{1}@@{a,b}{c}{z}=(1-% z)^{c-a-b}\,\HyperpFq{2}{1}@@{c-a,c-b}{c}{z}}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{\displaystyle{}{}\HyperpFq{2}{1}@@{a,b}{c}{z}=(1-%&#10;z)^{c-a-b}\,\HyperpFq{2}{1}@@{c-a,c-b}{c}{z}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.33" xref="p1.1.m1.1.33.1.cmml">
      <mrow id="p1.1.m1.1.33.2" xref="p1.1.m1.1.33.2.cmml">
        <mrow id="p1.1.m1.1.33.2.1" xref="p1.1.m1.1.33.2.1.1.cmml">
          <mrow id="p1.1.m1.1.33.2.1.2" xref="p1.1.m1.1.33.2.1.2.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">\HyperpFq</mtext>
            </merror>
            <mo id="p1.1.m1.1.33.2.1.2.1" xref="p1.1.m1.1.33.2.1.2.1.cmml">⁢</mo>
            <mn id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">21</mn>
            <mo id="p1.1.m1.1.33.2.1.2.1a" xref="p1.1.m1.1.33.2.1.2.1.cmml">⁢</mo>
            <mi mathvariant="normal" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">@</mi>
            <mo id="p1.1.m1.1.33.2.1.2.1b" xref="p1.1.m1.1.33.2.1.2.1.cmml">⁢</mo>
            <mi mathvariant="normal" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">@</mi>
            <mo id="p1.1.m1.1.33.2.1.2.1c" xref="p1.1.m1.1.33.2.1.2.1.cmml">⁢</mo>
            <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">a</mi>
          </mrow>
          <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.33.2.1.1.cmml">,</mo>
          <mrow id="p1.1.m1.1.33.2.1.3" xref="p1.1.m1.1.33.2.1.3.cmml">
            <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">b</mi>
            <mo id="p1.1.m1.1.33.2.1.3.1" xref="p1.1.m1.1.33.2.1.3.1.cmml">⁢</mo>
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">c</mi>
            <mo id="p1.1.m1.1.33.2.1.3.1a" xref="p1.1.m1.1.33.2.1.3.1.cmml">⁢</mo>
            <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">z</mi>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
        <mrow id="p1.1.m1.1.33.2.2" xref="p1.1.m1.1.33.2.2.cmml">
          <mrow id="p1.1.m1.1.33.2.2.1" xref="p1.1.m1.1.33.2.2.1.cmml">
            <mpadded width="+1.7pt" id="p1.1.m1.1.33.2.2.1.2" xref="p1.1.m1.1.33.2.2.1.2.cmml">
              <msup id="p1.1.m1.1.33.2.2.1.2a" xref="p1.1.m1.1.33.2.2.1.2.cmml">
                <mrow id="p1.1.m1.1.33.2.2.1.2.2" xref="p1.1.m1.1.33.2.2.1.2.2.2.cmml">
                  <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.33.2.2.1.2.2.2.cmml">(</mo>
                  <mrow id="p1.1.m1.1.33.2.2.1.2.2.2" xref="p1.1.m1.1.33.2.2.1.2.2.2.cmml">
                    <mn id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">1</mn>
                    <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">-</mo>
                    <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">z</mi>
                  </mrow>
                  <mo stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.33.2.2.1.2.2.2.cmml">)</mo>
                </mrow>
                <mrow id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">
                  <mi id="p1.1.m1.1.17.1.1" xref="p1.1.m1.1.17.1.1.cmml">c</mi>
                  <mo id="p1.1.m1.1.17.1.2" xref="p1.1.m1.1.17.1.2.cmml">-</mo>
                  <mi id="p1.1.m1.1.17.1.3" xref="p1.1.m1.1.17.1.3.cmml">a</mi>
                  <mo id="p1.1.m1.1.17.1.2a" xref="p1.1.m1.1.17.1.2.cmml">-</mo>
                  <mi id="p1.1.m1.1.17.1.5" xref="p1.1.m1.1.17.1.5.cmml">b</mi>
                </mrow>
              </msup>
            </mpadded>
            <mo id="p1.1.m1.1.33.2.2.1.1" xref="p1.1.m1.1.33.2.2.1.1.cmml">⁢</mo>
            <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.19" xref="p1.1.m1.1.19b.cmml">
              <mtext id="p1.1.m1.1.19a" xref="p1.1.m1.1.19b.cmml">\HyperpFq</mtext>
            </merror>
            <mo id="p1.1.m1.1.33.2.2.1.1a" xref="p1.1.m1.1.33.2.2.1.1.cmml">⁢</mo>
            <mn id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">21</mn>
            <mo id="p1.1.m1.1.33.2.2.1.1b" xref="p1.1.m1.1.33.2.2.1.1.cmml">⁢</mo>
            <mi mathvariant="normal" id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">@</mi>
            <mo id="p1.1.m1.1.33.2.2.1.1c" xref="p1.1.m1.1.33.2.2.1.1.cmml">⁢</mo>
            <mi mathvariant="normal" id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">@</mi>
            <mo id="p1.1.m1.1.33.2.2.1.1d" xref="p1.1.m1.1.33.2.2.1.1.cmml">⁢</mo>
            <mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">c</mi>
          </mrow>
          <mo id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">-</mo>
          <mi id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">a</mi>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.33.1a.cmml">,</mo>
      <mrow id="p1.1.m1.1.33.3" xref="p1.1.m1.1.33.3.cmml">
        <mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">c</mi>
        <mo id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">-</mo>
        <mrow id="p1.1.m1.1.33.3.1" xref="p1.1.m1.1.33.3.1.cmml">
          <mi id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">b</mi>
          <mo id="p1.1.m1.1.33.3.1.1" xref="p1.1.m1.1.33.3.1.1.cmml">⁢</mo>
          <mi id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">c</mi>
          <mo id="p1.1.m1.1.33.3.1.1a" xref="p1.1.m1.1.33.3.1.1.cmml">⁢</mo>
          <mi id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">z</mi>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.33.1.cmml" xref="p1.1.m1.1.33">
        <csymbol cd="ambiguous" id="p1.1.m1.1.33.1a.cmml" xref="p1.1.m1.1.27">formulae-sequence</csymbol>
        <apply id="p1.1.m1.1.33.2.cmml" xref="p1.1.m1.1.33.2">
          <eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
          <list id="p1.1.m1.1.33.2.1.1.cmml" xref="p1.1.m1.1.33.2.1">
            <apply id="p1.1.m1.1.33.2.1.2.cmml" xref="p1.1.m1.1.33.2.1.2">
              <times id="p1.1.m1.1.33.2.1.2.1.cmml" xref="p1.1.m1.1.33.2.1.2.1"/>
              <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">\HyperpFq</mtext>
                </merror>
              </ci>
              <cn type="integer" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">21</cn>
              <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">@</ci>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">@</ci>
              <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑎</ci>
            </apply>
            <apply id="p1.1.m1.1.33.2.1.3.cmml" xref="p1.1.m1.1.33.2.1.3">
              <times id="p1.1.m1.1.33.2.1.3.1.cmml" xref="p1.1.m1.1.33.2.1.3.1"/>
              <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝑏</ci>
              <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑐</ci>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑧</ci>
            </apply>
          </list>
          <apply id="p1.1.m1.1.33.2.2.cmml" xref="p1.1.m1.1.33.2.2">
            <minus id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25"/>
            <apply id="p1.1.m1.1.33.2.2.1.cmml" xref="p1.1.m1.1.33.2.2.1">
              <times id="p1.1.m1.1.33.2.2.1.1.cmml" xref="p1.1.m1.1.33.2.2.1.1"/>
              <apply id="p1.1.m1.1.33.2.2.1.2.cmml" xref="p1.1.m1.1.33.2.2.1.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.33.2.2.1.2.1.cmml" xref="p1.1.m1.1.33.2.2.1.2">superscript</csymbol>
                <apply id="p1.1.m1.1.33.2.2.1.2.2.2.cmml" xref="p1.1.m1.1.33.2.2.1.2.2">
                  <minus id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
                  <cn type="integer" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">1</cn>
                  <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝑧</ci>
                </apply>
                <apply id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">
                  <minus id="p1.1.m1.1.17.1.2.cmml" xref="p1.1.m1.1.17.1.2"/>
                  <ci id="p1.1.m1.1.17.1.1.cmml" xref="p1.1.m1.1.17.1.1">𝑐</ci>
                  <ci id="p1.1.m1.1.17.1.3.cmml" xref="p1.1.m1.1.17.1.3">𝑎</ci>
                  <ci id="p1.1.m1.1.17.1.5.cmml" xref="p1.1.m1.1.17.1.5">𝑏</ci>
                </apply>
              </apply>
              <ci id="p1.1.m1.1.19b.cmml" xref="p1.1.m1.1.19">
                <merror class="ltx_ERROR undefined undefined" id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
                  <mtext id="p1.1.m1.1.19a.cmml" xref="p1.1.m1.1.19">\HyperpFq</mtext>
                </merror>
              </ci>
              <cn type="integer" id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">21</cn>
              <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">@</ci>
              <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">@</ci>
              <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">𝑐</ci>
            </apply>
            <ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">𝑎</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.33.3.cmml" xref="p1.1.m1.1.33.3">
          <minus id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29"/>
          <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">𝑐</ci>
          <apply id="p1.1.m1.1.33.3.1.cmml" xref="p1.1.m1.1.33.3.1">
            <times id="p1.1.m1.1.33.3.1.1.cmml" xref="p1.1.m1.1.33.3.1.1"/>
            <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">𝑏</ci>
            <ci id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31">𝑐</ci>
            <ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">𝑧</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle{\displaystyle{}{}\HyperpFq{2}{1}@@{a,b}{c}{z}=(1-%
z)^{c-a-b}\,\HyperpFq{2}{1}@@{c-a,c-b}{c}{z}}}}</annotation>
  </semantics>
</math>

SVG (13.282 KB / 3.676 KB) :

{\displaystyle{\displaystyle{\displaystyle{}{}\HyperpFq{2}{1}@@{a,b}{c}{z}=(1-% z)^{c-a-b}\,\HyperpFq{2}{1}@@{c-a,c-b}{c}{z}}}}

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

[ffceef7933b3ea77c2196a36] /index.php?title=Special:FormulaInfo&pid=3121&eid=math.3121.0 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:01.13:04 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"