Jump to navigation Jump to search

General

Display information for equation id:math.237599.13 on revision:237599

* Page found: Selection rule (eq math.237599.13)

(force rerendering)

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

Occurrences on the following pages:

Hash: afa56db8578a76412f10e5c959cac759

TeX (original user input):

\pi(\mathrm{M}\lambda) = \pi_{\mathrm{i}} \pi_{\mathrm{f}} = (-1)^{\lambda+1}\,.

TeX (checked):

\pi (\mathrm {M} \lambda )=\pi _{\mathrm {i} }\pi _{\mathrm {f} }=(-1)^{\lambda +1}\,.

LaTeXML (experimental; uses MathML) rendering

MathML (5.931 KB / 1.05 KB) :

π ( M λ ) = π i π f = ( - 1 ) λ + 1 . 𝜋 M 𝜆 subscript 𝜋 i subscript 𝜋 f superscript 1 𝜆 1 {\displaystyle\pi({\mathrm{M}}\lambda)=\pi_{{{\mathrm{i}}}}\pi_{{{\mathrm{f}}}% }=(-1)^{{\lambda+1}}\,.}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\pi({\mathrm{M}}\lambda)=\pi_{{{\mathrm{i}}}}\pi_{{{\mathrm{f}}}%&#10;}=(-1)^{{\lambda+1}}\,.}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.19" xref="p1.1.m1.1.19.2.cmml">
      <mrow id="p1.1.m1.1.19.2" xref="p1.1.m1.1.19.2.cmml">
        <mrow id="p1.1.m1.1.19.2.2" xref="p1.1.m1.1.19.2.2.cmml">
          <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">π</mi>
          <mo id="p1.1.m1.1.19.2.2.1" xref="p1.1.m1.1.19.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.19.2.2.2" xref="p1.1.m1.1.19.2.2.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.19.2.2.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.19.2.2.2.2" xref="p1.1.m1.1.19.2.2.2.2.cmml">
              <mi mathvariant="normal" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">M</mi>
              <mo id="p1.1.m1.1.19.2.2.2.2.1" xref="p1.1.m1.1.19.2.2.2.2.1.cmml"></mo>
              <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">λ</mi>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.19.2.2.2.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
        <mrow id="p1.1.m1.1.19.2.3" xref="p1.1.m1.1.19.2.3.cmml">
          <msub id="p1.1.m1.1.19.2.3.2" xref="p1.1.m1.1.19.2.3.2.cmml">
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">π</mi>
            <mi mathvariant="normal" id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">i</mi>
          </msub>
          <mo id="p1.1.m1.1.19.2.3.1" xref="p1.1.m1.1.19.2.3.1.cmml"></mo>
          <msub id="p1.1.m1.1.19.2.3.3" xref="p1.1.m1.1.19.2.3.3.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">π</mi>
            <mi mathvariant="normal" id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">f</mi>
          </msub>
        </mrow>
        <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
        <mpadded width="+1.7pt" id="p1.1.m1.1.19.2.4" xref="p1.1.m1.1.19.2.4.cmml">
          <msup id="p1.1.m1.1.19.2.4a" xref="p1.1.m1.1.19.2.4.cmml">
            <mrow id="p1.1.m1.1.19.2.4.2" xref="p1.1.m1.1.19.2.4.2.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.19.2.4.2.2.cmml">(</mo>
              <mrow id="p1.1.m1.1.19.2.4.2.2" xref="p1.1.m1.1.19.2.4.2.2.cmml">
                <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">-</mo>
                <mn id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">1</mn>
              </mrow>
              <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.19.2.4.2.2.cmml">)</mo>
            </mrow>
            <mrow id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">
              <mi id="p1.1.m1.1.16.1.1" xref="p1.1.m1.1.16.1.1.cmml">λ</mi>
              <mo id="p1.1.m1.1.16.1.2" xref="p1.1.m1.1.16.1.2.cmml">+</mo>
              <mn id="p1.1.m1.1.16.1.3" xref="p1.1.m1.1.16.1.3.cmml">1</mn>
            </mrow>
          </msup>
        </mpadded>
      </mrow>
      <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.19.2.cmml">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.19.2.cmml" xref="p1.1.m1.1.19">
        <and id="p1.1.m1.1.19.2a.cmml" xref="p1.1.m1.1.19"/>
        <apply id="p1.1.m1.1.19.2b.cmml" xref="p1.1.m1.1.19">
          <eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
          <apply id="p1.1.m1.1.19.2.2.cmml" xref="p1.1.m1.1.19.2.2">
            <times id="p1.1.m1.1.19.2.2.1.cmml" xref="p1.1.m1.1.19.2.2.1"/>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝜋</ci>
            <apply id="p1.1.m1.1.19.2.2.2.2.cmml" xref="p1.1.m1.1.19.2.2.2">
              <times id="p1.1.m1.1.19.2.2.2.2.1.cmml" xref="p1.1.m1.1.19.2.2.2.2.1"/>
              <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">M</ci>
              <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝜆</ci>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.19.2.3.cmml" xref="p1.1.m1.1.19.2.3">
            <times id="p1.1.m1.1.19.2.3.1.cmml" xref="p1.1.m1.1.19.2.3.1"/>
            <apply id="p1.1.m1.1.19.2.3.2.cmml" xref="p1.1.m1.1.19.2.3.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.19.2.3.2.1.cmml" xref="p1.1.m1.1.19.2.3.2">subscript</csymbol>
              <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝜋</ci>
              <ci id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">i</ci>
            </apply>
            <apply id="p1.1.m1.1.19.2.3.3.cmml" xref="p1.1.m1.1.19.2.3.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.19.2.3.3.1.cmml" xref="p1.1.m1.1.19.2.3.3">subscript</csymbol>
              <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝜋</ci>
              <ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">f</ci>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.19.2c.cmml" xref="p1.1.m1.1.19">
          <eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
          <share href="#p1.1.m1.1.19.2.3.cmml" id="p1.1.m1.1.19.2d.cmml" xref="p1.1.m1.1.19"/>
          <apply id="p1.1.m1.1.19.2.4.cmml" xref="p1.1.m1.1.19.2.4">
            <csymbol cd="ambiguous" id="p1.1.m1.1.19.2.4.1.cmml" xref="p1.1.m1.1.19.2.4">superscript</csymbol>
            <apply id="p1.1.m1.1.19.2.4.2.2.cmml" xref="p1.1.m1.1.19.2.4.2">
              <minus id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
              <cn type="integer" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">1</cn>
            </apply>
            <apply id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">
              <plus id="p1.1.m1.1.16.1.2.cmml" xref="p1.1.m1.1.16.1.2"/>
              <ci id="p1.1.m1.1.16.1.1.cmml" xref="p1.1.m1.1.16.1.1">𝜆</ci>
              <cn type="integer" id="p1.1.m1.1.16.1.3.cmml" xref="p1.1.m1.1.16.1.3">1</cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\pi({\mathrm{M}}\lambda)=\pi_{{{\mathrm{i}}}}\pi_{{{\mathrm{f}}}%
}=(-1)^{{\lambda+1}}\,.}</annotation>
  </semantics>
</math>

SVG (7.87 KB / 2.621 KB) :

pi times left-parenthesis normal upper M times lamda right-parenthesis equals pi Subscript normal i Baseline times pi Subscript normal f Baseline equals left-parenthesis negative 1 right-parenthesis Superscript lamda plus 1 Baseline period

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: pi*(M*lambda)= pi[i]*pi[f]=(- 1)^(lambda + 1)

Information about the conversion process:

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Maple uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!
Use the DLMF-Macro \cpi to translate \pi as a constant.


i: the imaginary unit == the principal square root of -1 was translated to: i


Translation to Mathematica

In Mathematica: \[Pi]*(M*\[Lambda])= Subscript[\[Pi], i]*Subscript[\[Pi], f]=(- 1)^(\[Lambda]+ 1)

Information about the conversion process:

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Mathematica uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!
Use the DLMF-Macro \cpi to translate \pi as a constant.


i: the imaginary unit == the principal square root of -1 was translated to: i


Similar pages

Calculated based on the variables occurring on the entire Selection rule page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results