Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.2718.31 on revision:2718

* Page found: Fermis Goldene Regel (eq math.2718.31)

(force rerendering)

Occurrences on the following pages:

Hash: 9d0b5c63c6c094f12264f4a833b74084

TeX (original user input):

\int\limits_{-\infty }^{\infty }{dx\operatorname{sinc}\left( x \right)}=\int\limits_{-\infty }^{\infty }{dx{{\operatorname{sinc}}^{2}}\left( x \right)}=\pi

TeX (checked):

\int \limits _{-\infty }^{\infty }{dx\operatorname {sinc} \left(x\right)}=\int \limits _{-\infty }^{\infty }{dx{{\operatorname {sinc} }^{2}}\left(x\right)}=\pi

LaTeXML (experimentell; verwendet MathML) rendering

MathML (8.408 KB / 1.324 KB) :

- 𝑑 x sinc ( x ) = - 𝑑 x sinc 2 ( x ) = π superscript subscript differential-d 𝑥 sinc 𝑥 superscript subscript differential-d 𝑥 superscript sinc 2 𝑥 𝜋 {\displaystyle{\displaystyle\int\limits_{-\infty}^{\infty}{dx\operatorname{% sinc}\left(x\right)}=\int\limits_{-\infty}^{\infty}{dx{{\operatorname{sinc}}^{% 2}}\left(x\right)}=\pi}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\int\limits_{-\infty}^{\infty}{dx\operatorname{%&#10;sinc}\left(x\right)}=\int\limits_{-\infty}^{\infty}{dx{{\operatorname{sinc}}^{%&#10;2}}\left(x\right)}=\pi}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">
      <mrow id="p1.1.m1.1.29.2" xref="p1.1.m1.1.29.2.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.29.2.1" xref="p1.1.m1.1.29.2.1.cmml">
          <munderover id="p1.1.m1.1.29.2.1a" xref="p1.1.m1.1.29.2.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml"></mo>
            <mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
              <mo id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">-</mo>
              <mi mathvariant="normal" id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml"></mi>
            </mrow>
            <mi mathvariant="normal" id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml"></mi>
          </munderover>
        </mstyle>
        <mrow id="p1.1.m1.1.29.2.2" xref="p1.1.m1.1.29.2.2.cmml">
          <mrow id="p1.1.m1.1.29.2.2.2" xref="p1.1.m1.1.29.2.2.2.cmml">
            <mo rspace="0pt" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">𝑑</mo>
            <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">x</mi>
          </mrow>
          <mo id="p1.1.m1.1.29.2.2.1" xref="p1.1.m1.1.29.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.29.2.2.3.2" xref="p1.1.m1.1.29.2.2.3.1.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">sinc</mi>
            <mo id="p1.1.m1.1.29.2.2.3.2a" xref="p1.1.m1.1.29.2.2.3.1.cmml"></mo>
            <mrow id="p1.1.m1.1.29.2.2.3.2.1" xref="p1.1.m1.1.29.2.2.3.1.cmml">
              <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.29.2.2.3.1.cmml">(</mo>
              <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">x</mi>
              <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.29.2.2.3.1.cmml">)</mo>
            </mrow>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">=</mo>
      <mrow id="p1.1.m1.1.29.3" xref="p1.1.m1.1.29.3.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.29.3.1" xref="p1.1.m1.1.29.3.1.cmml">
          <munderover id="p1.1.m1.1.29.3.1a" xref="p1.1.m1.1.29.3.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml"></mo>
            <mrow id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
              <mo id="p1.1.m1.1.15.1.1" xref="p1.1.m1.1.15.1.1.cmml">-</mo>
              <mi mathvariant="normal" id="p1.1.m1.1.15.1.2" xref="p1.1.m1.1.15.1.2.cmml"></mi>
            </mrow>
            <mi mathvariant="normal" id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml"></mi>
          </munderover>
        </mstyle>
        <mrow id="p1.1.m1.1.29.3.2" xref="p1.1.m1.1.29.3.2.cmml">
          <mrow id="p1.1.m1.1.29.3.2.2" xref="p1.1.m1.1.29.3.2.2.cmml">
            <mo rspace="0pt" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">𝑑</mo>
            <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">x</mi>
          </mrow>
          <mo id="p1.1.m1.1.29.3.2.1" xref="p1.1.m1.1.29.3.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.29.3.2.3.2" xref="p1.1.m1.1.29.3.2.3.1.cmml">
            <msup id="p1.1.m1.1.29.3.2.3.2.1" xref="p1.1.m1.1.29.3.2.3.2.1.cmml">
              <mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">sinc</mi>
              <mn id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">2</mn>
            </msup>
            <mo id="p1.1.m1.1.29.3.2.3.2a" xref="p1.1.m1.1.29.3.2.3.1.cmml"></mo>
            <mrow id="p1.1.m1.1.29.3.2.3.2.2" xref="p1.1.m1.1.29.3.2.3.1.cmml">
              <mo id="p1.1.m1.1.24" xref="p1.1.m1.1.29.3.2.3.1.cmml">(</mo>
              <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">x</mi>
              <mo id="p1.1.m1.1.26" xref="p1.1.m1.1.29.3.2.3.1.cmml">)</mo>
            </mrow>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">=</mo>
      <mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">π</mi>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">
        <and id="p1.1.m1.1.29a.cmml" xref="p1.1.m1.1.29"/>
        <apply id="p1.1.m1.1.29b.cmml" xref="p1.1.m1.1.29">
          <eq id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
          <apply id="p1.1.m1.1.29.2.cmml" xref="p1.1.m1.1.29.2">
            <apply id="p1.1.m1.1.29.2.1.cmml" xref="p1.1.m1.1.29.2.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.29.2.1.1.cmml" xref="p1.1.m1.1.29.2.1">superscript</csymbol>
              <apply id="p1.1.m1.1.29.2.1.2.cmml" xref="p1.1.m1.1.29.2.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.29.2.1.2.1.cmml" xref="p1.1.m1.1.29.2.1">subscript</csymbol>
                <int id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
                <apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
                  <minus id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1"/>
                  <infinity id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2"/>
                </apply>
              </apply>
              <infinity id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1"/>
            </apply>
            <apply id="p1.1.m1.1.29.2.2.cmml" xref="p1.1.m1.1.29.2.2">
              <times id="p1.1.m1.1.29.2.2.1.cmml" xref="p1.1.m1.1.29.2.2.1"/>
              <apply id="p1.1.m1.1.29.2.2.2.cmml" xref="p1.1.m1.1.29.2.2.2">
                <csymbol cd="latexml" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">differential-d</csymbol>
                <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑥</ci>
              </apply>
              <apply id="p1.1.m1.1.29.2.2.3.1.cmml" xref="p1.1.m1.1.29.2.2.3.2">
                <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">sinc</ci>
                <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝑥</ci>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.29.3.cmml" xref="p1.1.m1.1.29.3">
            <apply id="p1.1.m1.1.29.3.1.cmml" xref="p1.1.m1.1.29.3.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.29.3.1.1.cmml" xref="p1.1.m1.1.29.3.1">superscript</csymbol>
              <apply id="p1.1.m1.1.29.3.1.2.cmml" xref="p1.1.m1.1.29.3.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.29.3.1.2.1.cmml" xref="p1.1.m1.1.29.3.1">subscript</csymbol>
                <int id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
                <apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
                  <minus id="p1.1.m1.1.15.1.1.cmml" xref="p1.1.m1.1.15.1.1"/>
                  <infinity id="p1.1.m1.1.15.1.2.cmml" xref="p1.1.m1.1.15.1.2"/>
                </apply>
              </apply>
              <infinity id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1"/>
            </apply>
            <apply id="p1.1.m1.1.29.3.2.cmml" xref="p1.1.m1.1.29.3.2">
              <times id="p1.1.m1.1.29.3.2.1.cmml" xref="p1.1.m1.1.29.3.2.1"/>
              <apply id="p1.1.m1.1.29.3.2.2.cmml" xref="p1.1.m1.1.29.3.2.2">
                <csymbol cd="latexml" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">differential-d</csymbol>
                <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝑥</ci>
              </apply>
              <apply id="p1.1.m1.1.29.3.2.3.1.cmml" xref="p1.1.m1.1.29.3.2.3.2">
                <apply id="p1.1.m1.1.29.3.2.3.2.1.cmml" xref="p1.1.m1.1.29.3.2.3.2.1">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.29.3.2.3.2.1.1.cmml" xref="p1.1.m1.1.29.3.2.3.2.1">superscript</csymbol>
                  <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">sinc</ci>
                  <cn type="integer" id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">2</cn>
                </apply>
                <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">𝑥</ci>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.29c.cmml" xref="p1.1.m1.1.29">
          <eq id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27"/>
          <share href="#p1.1.m1.1.29.3.cmml" id="p1.1.m1.1.29d.cmml" xref="p1.1.m1.1.29"/>
          <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">𝜋</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\int\limits_{-\infty}^{\infty}{dx\operatorname{%
sinc}\left(x\right)}=\int\limits_{-\infty}^{\infty}{dx{{\operatorname{sinc}}^{%
2}}\left(x\right)}=\pi}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (1.271 KB / 325 B) :

dxsinc(x)=dxsinc2(x)=π
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi mathvariant="normal">&#x221E;</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>x</mi><mi data-mjx-texclass="OP" mathvariant="normal">sinc</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi mathvariant="normal">&#x221E;</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>x</mi><msup><mi data-mjx-texclass="OP" mathvariant="normal">sinc</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>=</mo><mi>&#x03C0;</mi></mstyle></mrow></math>

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 Fermis Goldene Regel page

Identifiers

  • x
  • x
  • x
  • x
  • π

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results