Jump to navigation Jump to search

General

Display information for equation id:math.63472.95 on revision:63472

* Page found: Results of Bernoulli and Euler Polynomials (eq math.63472.95)

(force rerendering)

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

Occurrences on the following pages:

Hash: f1504a3422a22db703f2dceb32aa2f2b

TeX (original user input):

G_{n} = 2(1-2^{n})\BernoullinumberB{n}

TeX (checked):

LaTeXML (experimental; uses MathML) rendering

MathML (3.421 KB / 766 B) :

G n = 2 ( 1 - 2 n ) B n subscript 𝐺 𝑛 2 1 superscript 2 𝑛 Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle G_{n}=2(1-2^{n})B_{n}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle G_{n}=2(1-2^{n})B_{n}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
      <msub id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">G</mi>
        <mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">n</mi>
      </msub>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
      <mrow id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">
        <mn id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">2</mn>
        <mo id="p1.1.m1.1.12.2.1" xref="p1.1.m1.1.12.2.1.cmml"></mo>
        <mrow id="p1.1.m1.1.12.2.2" xref="p1.1.m1.1.12.2.2.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.12.2.2.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.12.2.2.2" xref="p1.1.m1.1.12.2.2.2.cmml">
            <mn id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">1</mn>
            <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">-</mo>
            <msup id="p1.1.m1.1.12.2.2.2.1" xref="p1.1.m1.1.12.2.2.2.1.cmml">
              <mn id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">2</mn>
              <mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">n</mi>
            </msup>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.12.2.2.2.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.12.2.1a" xref="p1.1.m1.1.12.2.1.cmml"></mo>
        <msub id="p1.1.m1.1.11.4" xref="p1.1.m1.1.11.1.cmml">
          <mi id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.1.1.cmml">B</mi>
          <mi id="p1.1.m1.1.11.3.1" xref="p1.1.m1.1.11.3.1.cmml">n</mi>
        </msub>
      </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.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
        <apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
          <csymbol cd="ambiguous" id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1">subscript</csymbol>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝐺</ci>
          <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝑛</ci>
        </apply>
        <apply id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2">
          <times id="p1.1.m1.1.12.2.1.cmml" xref="p1.1.m1.1.12.2.1"/>
          <cn type="integer" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">2</cn>
          <apply id="p1.1.m1.1.12.2.2.2.cmml" xref="p1.1.m1.1.12.2.2">
            <minus id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
            <cn type="integer" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">1</cn>
            <apply id="p1.1.m1.1.12.2.2.2.1.cmml" xref="p1.1.m1.1.12.2.2.2.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.12.2.2.2.1.1.cmml" xref="p1.1.m1.1.12.2.2.2.1">superscript</csymbol>
              <cn type="integer" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">2</cn>
              <ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">𝑛</ci>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.4">
            <csymbol cd="dlmf" id="p1.1.m1.1.11.1.1.cmml" xref="p1.1.m1.1.11.2">Bernoulli-number-B</csymbol>
            <ci id="p1.1.m1.1.11.3.1.cmml" xref="p1.1.m1.1.11.3.1">𝑛</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle G_{n}=2(1-2^{n})B_{n}}}</annotation>
  </semantics>
</math>

SVG (6.403 KB / 2.475 KB) :

{\displaystyle{\displaystyle G_{n}=2(1-2^{n})B_{n}}}

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

[7a140078acf88611778d3098] /index.php?title=Special:FormulaInfo&pid=63472&eid=math.63472.95 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 Bernoulli and Euler Polynomials page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results