Jump to navigation Jump to search

General

Display information for equation id:math.225421.0 on revision:225421

* Page found: Empty product (eq math.225421.0)

(force rerendering)

Occurrences on the following pages:

Hash: dc23fc9e7ce3c0a16a23577320262ffb

TeX (original user input): 

P_m = \prod_{i=1}^m a_i = a_1 \cdots  a_m

TeX (checked): 

P_{m}=\prod _{i=1}^{m}a_{i}=a_{1}\cdots a_{m}

LaTeXML (experimental; uses MathML) rendering

MathML (5.543 KB / 1.046 KB) :

P m = ∏ i = 1 m a i = a 1 ⁢ ⋯ ⁢ a m subscript 𝑃 𝑚 superscript subscript product 𝑖 1 𝑚 subscript 𝑎 𝑖 subscript 𝑎 1 ⋯ subscript 𝑎 𝑚 {\displaystyle{\displaystyle P_{m}=\prod_{i=1}^{m}a_{i}=a_{1}\cdots a_{m}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle P_{m}=\prod_{i=1}^{m}a_{i}=a_{1}\cdots a_{m}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
      <msub id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">P</mi>
        <mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">m</mi>
      </msub>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
      <mrow id="p1.1.m1.1.15.3" xref="p1.1.m1.1.15.3.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.15.3.1" xref="p1.1.m1.1.15.3.1.cmml">
          <munderover id="p1.1.m1.1.15.3.1a" xref="p1.1.m1.1.15.3.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">∏</mo>
            <mrow id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">
              <mi id="p1.1.m1.1.5.1.1" xref="p1.1.m1.1.5.1.1.cmml">i</mi>
              <mo id="p1.1.m1.1.5.1.2" xref="p1.1.m1.1.5.1.2.cmml">=</mo>
              <mn id="p1.1.m1.1.5.1.3" xref="p1.1.m1.1.5.1.3.cmml">1</mn>
            </mrow>
            <mi id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">m</mi>
          </munderover>
        </mstyle>
        <msub id="p1.1.m1.1.15.3.2" xref="p1.1.m1.1.15.3.2.cmml">
          <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">a</mi>
          <mi id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">i</mi>
        </msub>
      </mrow>
      <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">=</mo>
      <mrow id="p1.1.m1.1.15.4" xref="p1.1.m1.1.15.4.cmml">
        <msub id="p1.1.m1.1.15.4.2" xref="p1.1.m1.1.15.4.2.cmml">
          <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">a</mi>
          <mn id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">1</mn>
        </msub>
        <mo id="p1.1.m1.1.15.4.1" xref="p1.1.m1.1.15.4.1.cmml">⁢</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">⋯</mi>
        <mo id="p1.1.m1.1.15.4.1a" xref="p1.1.m1.1.15.4.1.cmml">⁢</mo>
        <msub id="p1.1.m1.1.15.4.3" xref="p1.1.m1.1.15.4.3.cmml">
          <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">a</mi>
          <mi id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">m</mi>
        </msub>
      </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">
        <and id="p1.1.m1.1.15a.cmml" xref="p1.1.m1.1.15"/>
        <apply id="p1.1.m1.1.15b.cmml" xref="p1.1.m1.1.15">
          <eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
          <apply id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.15.2.1.cmml" xref="p1.1.m1.1.15.2">subscript</csymbol>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑃</ci>
            <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝑚</ci>
          </apply>
          <apply id="p1.1.m1.1.15.3.cmml" xref="p1.1.m1.1.15.3">
            <apply id="p1.1.m1.1.15.3.1.cmml" xref="p1.1.m1.1.15.3.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.3.1.1.cmml" xref="p1.1.m1.1.15.3.1">superscript</csymbol>
              <apply id="p1.1.m1.1.15.3.1.2.cmml" xref="p1.1.m1.1.15.3.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.15.3.1.2.1.cmml" xref="p1.1.m1.1.15.3.1">subscript</csymbol>
                <csymbol cd="latexml" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">product</csymbol>
                <apply id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">
                  <eq id="p1.1.m1.1.5.1.2.cmml" xref="p1.1.m1.1.5.1.2"/>
                  <ci id="p1.1.m1.1.5.1.1.cmml" xref="p1.1.m1.1.5.1.1">𝑖</ci>
                  <cn type="integer" id="p1.1.m1.1.5.1.3.cmml" xref="p1.1.m1.1.5.1.3">1</cn>
                </apply>
              </apply>
              <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">𝑚</ci>
            </apply>
            <apply id="p1.1.m1.1.15.3.2.cmml" xref="p1.1.m1.1.15.3.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.3.2.1.cmml" xref="p1.1.m1.1.15.3.2">subscript</csymbol>
              <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝑎</ci>
              <ci id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">𝑖</ci>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.15c.cmml" xref="p1.1.m1.1.15">
          <eq id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
          <share href="#p1.1.m1.1.15.3.cmml" id="p1.1.m1.1.15d.cmml" xref="p1.1.m1.1.15"/>
          <apply id="p1.1.m1.1.15.4.cmml" xref="p1.1.m1.1.15.4">
            <times id="p1.1.m1.1.15.4.1.cmml" xref="p1.1.m1.1.15.4.1"/>
            <apply id="p1.1.m1.1.15.4.2.cmml" xref="p1.1.m1.1.15.4.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.4.2.1.cmml" xref="p1.1.m1.1.15.4.2">subscript</csymbol>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑎</ci>
              <cn type="integer" id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">1</cn>
            </apply>
            <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">⋯</ci>
            <apply id="p1.1.m1.1.15.4.3.cmml" xref="p1.1.m1.1.15.4.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.4.3.1.cmml" xref="p1.1.m1.1.15.4.3">subscript</csymbol>
              <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝑎</ci>
              <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">𝑚</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle P_{m}=\prod_{i=1}^{m}a_{i}=a_{1}\cdots a_{m}}}</annotation>
  </semantics>
</math>

SVG (7.244 KB / 2.618 KB) :

upper P Subscript m Baseline equals product Underscript i equals 1 Overscript m Endscripts a Subscript i Baseline equals a 1 times midline-horizontal-ellipsis times a Subscript m

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (1.282 KB / 385 B) :

P m = ∏ i = 1 m a i = a 1 ⋯ a m {\displaystyle P_{m}=\prod _{i=1}^{m}a_{i}=a_{1}\cdots a_{m}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle P_{m}=\prod _{i=1}^{m}a_{i}=a_{1}\cdots a_{m}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>P</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>m</mi>
          </mrow>
        </msub>
        <mo>=</mo>
        <munderover>
          <mo>&#x220F;<!-- ∏ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>i</mi>
            <mo>=</mo>
            <mn>1</mn>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>m</mi>
          </mrow>
        </munderover>
        <msub>
          <mi>a</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>i</mi>
          </mrow>
        </msub>
        <mo>=</mo>
        <msub>
          <mi>a</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>1</mn>
          </mrow>
        </msub>
        <mo>&#x22EF;<!-- ⋯ --></mo>
        <msub>
          <mi>a</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>m</mi>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle P_{m}=\prod _{i=1}^{m}a_{i}=a_{1}\cdots a_{m}}</annotation>
  </semantics>
</math>

SVG (5.617 KB / 2.375 KB) :

{\displaystyle P_{m}=\prod _{i=1}^{m}a_{i}=a_{1}\cdots a_{m}}

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 Empty product page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "https://en.formulasearchengine.com/wiki/Special:FormulaInfo"