Jump to navigation Jump to search

General

Display information for equation id:KLS:01.01:02 on revision:1983

* Page found: Orthogonal polynomials (eq KLS:01.01:02)

(force rerendering)

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

Occurrences on the following pages:

Hash: 472352d3911e73c5572293d9113d1292

TeX (original user input):

{\displaystyle 
0<\int_a^bx^{2n}w(x)\,dx<\infty\quad\textrm{for all}
}

TeX (checked):

{\displaystyle 0<\int _{a}^{b}x^{2n}w(x)\,dx<\infty \quad {\textrm {forall}}}

LaTeXML (experimental; uses MathML) rendering

MathML (6.07 KB / 1.183 KB) :

0 < a b x 2 n w ( x ) 𝑑 x < for all formulae-sequence 0 superscript subscript 𝑎 𝑏 superscript 𝑥 2 𝑛 𝑤 𝑥 differential-d 𝑥 for all {\displaystyle{\displaystyle{\displaystyle 0<\int_{a}^{b}x^{2n}w(x)\,dx<\infty% \quad\textrm{for all}}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{\displaystyle 0&lt;\int_{a}^{b}x^{2n}w(x)\,dx&lt;\infty%&#10;\quad\textrm{for all}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.20" xref="p1.1.m1.1.20.1.cmml">
      <mrow id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">
        <mn id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">0</mn>
        <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">&lt;</mo>
        <mrow id="p1.1.m1.1.20.2.2" xref="p1.1.m1.1.20.2.2.cmml">
          <mstyle displaystyle="true" id="p1.1.m1.1.20.2.2.1" xref="p1.1.m1.1.20.2.2.1.cmml">
            <msubsup id="p1.1.m1.1.20.2.2.1a" xref="p1.1.m1.1.20.2.2.1.cmml">
              <mo largeop="true" symmetric="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml"></mo>
              <mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">a</mi>
              <mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">b</mi>
            </msubsup>
          </mstyle>
          <mrow id="p1.1.m1.1.20.2.2.2" xref="p1.1.m1.1.20.2.2.2.cmml">
            <msup id="p1.1.m1.1.20.2.2.2.2" xref="p1.1.m1.1.20.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">x</mi>
              <mrow id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">
                <mn id="p1.1.m1.1.7.1.1" xref="p1.1.m1.1.7.1.1.cmml">2</mn>
                <mo id="p1.1.m1.1.7.1.3" xref="p1.1.m1.1.7.1.3.cmml"></mo>
                <mi id="p1.1.m1.1.7.1.2" xref="p1.1.m1.1.7.1.2.cmml">n</mi>
              </mrow>
            </msup>
            <mo id="p1.1.m1.1.20.2.2.2.1" xref="p1.1.m1.1.20.2.2.2.1.cmml"></mo>
            <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">w</mi>
            <mo id="p1.1.m1.1.20.2.2.2.1a" xref="p1.1.m1.1.20.2.2.2.1.cmml"></mo>
            <mrow id="p1.1.m1.1.20.2.2.2.3" xref="p1.1.m1.1.20.2.2.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.20.2.2.2.cmml">(</mo>
              <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">x</mi>
              <mo rspace="4.2pt" stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.20.2.2.2.cmml">)</mo>
            </mrow>
            <mo id="p1.1.m1.1.20.2.2.2.1b" xref="p1.1.m1.1.20.2.2.2.1.cmml"></mo>
            <mrow id="p1.1.m1.1.20.2.2.2.4" xref="p1.1.m1.1.20.2.2.2.4.cmml">
              <mo rspace="0pt" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">𝑑</mo>
              <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">x</mi>
            </mrow>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">&lt;</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml"></mi>
      </mrow>
      <mo mathvariant="italic" separator="true" id="p1.1.m1.1.19" xref="p1.1.m1.1.20.1a.cmml"></mo>
      <mtext id="p1.1.m1.1.18" xref="p1.1.m1.1.18a.cmml">for all</mtext>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20">
        <csymbol cd="ambiguous" id="p1.1.m1.1.20.1a.cmml" xref="p1.1.m1.1.19">formulae-sequence</csymbol>
        <apply id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">
          <and id="p1.1.m1.1.20.2a.cmml" xref="p1.1.m1.1.20.2"/>
          <apply id="p1.1.m1.1.20.2b.cmml" xref="p1.1.m1.1.20.2">
            <lt id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
            <cn type="integer" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">0</cn>
            <apply id="p1.1.m1.1.20.2.2.cmml" xref="p1.1.m1.1.20.2.2">
              <apply id="p1.1.m1.1.20.2.2.1.cmml" xref="p1.1.m1.1.20.2.2.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.20.2.2.1.1.cmml" xref="p1.1.m1.1.20.2.2.1">superscript</csymbol>
                <apply id="p1.1.m1.1.20.2.2.1.2.cmml" xref="p1.1.m1.1.20.2.2.1">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.20.2.2.1.2.1.cmml" xref="p1.1.m1.1.20.2.2.1">subscript</csymbol>
                  <int id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
                  <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">𝑎</ci>
                </apply>
                <ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">𝑏</ci>
              </apply>
              <apply id="p1.1.m1.1.20.2.2.2.cmml" xref="p1.1.m1.1.20.2.2.2">
                <times id="p1.1.m1.1.20.2.2.2.1.cmml" xref="p1.1.m1.1.20.2.2.2.1"/>
                <apply id="p1.1.m1.1.20.2.2.2.2.cmml" xref="p1.1.m1.1.20.2.2.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.20.2.2.2.2.1.cmml" xref="p1.1.m1.1.20.2.2.2.2">superscript</csymbol>
                  <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑥</ci>
                  <apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
                    <times id="p1.1.m1.1.7.1.3.cmml" xref="p1.1.m1.1.7.1.3"/>
                    <cn type="integer" id="p1.1.m1.1.7.1.1.cmml" xref="p1.1.m1.1.7.1.1">2</cn>
                    <ci id="p1.1.m1.1.7.1.2.cmml" xref="p1.1.m1.1.7.1.2">𝑛</ci>
                  </apply>
                </apply>
                <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝑤</ci>
                <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑥</ci>
                <apply id="p1.1.m1.1.20.2.2.2.4.cmml" xref="p1.1.m1.1.20.2.2.2.4">
                  <csymbol cd="latexml" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">differential-d</csymbol>
                  <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑥</ci>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.20.2c.cmml" xref="p1.1.m1.1.20.2">
            <lt id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
            <share href="#p1.1.m1.1.20.2.2.cmml" id="p1.1.m1.1.20.2d.cmml" xref="p1.1.m1.1.20.2"/>
            <infinity id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
          </apply>
        </apply>
        <ci id="p1.1.m1.1.18a.cmml" xref="p1.1.m1.1.18">
          <mtext id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">for all</mtext>
        </ci>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle{\displaystyle 0&lt;\int_{a}^{b}x^{2n}w(x)\,dx&lt;\infty%
\quad\textrm{for all}}}}</annotation>
  </semantics>
</math>

SVG (12.949 KB / 4.934 KB) :

{\displaystyle{\displaystyle{\displaystyle 0<\int_{a}^{b}x^{2n}w(x)\,dx<\infty% \quad\textrm{for all}}}}

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

MathML (1.596 KB / 494 B) :

0 < a b x 2 n w ( x ) d x < forall {\displaystyle {\displaystyle 0<\int _{a}^{b}x^{2n}w(x)\,dx<\infty \quad {\textrm {forall}}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\displaystyle 0&lt;\int _{a}^{b}x^{2n}w(x)\,dx&lt;\infty \quad {\textrm {forall}}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mstyle displaystyle="true" scriptlevel="0">
            <mn>0</mn>
            <mo>&lt;</mo>
            <msubsup>
              <mo>&#x222B;<!-- ∫ --></mo>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>a</mi>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>b</mi>
              </mrow>
            </msubsup>
            <msup>
              <mi>x</mi>
              <mrow class="MJX-TeXAtom-ORD">
                <mn>2</mn>
                <mi>n</mi>
              </mrow>
            </msup>
            <mi>w</mi>
            <mo stretchy="false">(</mo>
            <mi>x</mi>
            <mo stretchy="false">)</mo>
            <mspace width="thinmathspace" />
            <mi>d</mi>
            <mi>x</mi>
            <mo>&lt;</mo>
            <mi mathvariant="normal">&#x221E;<!-- ∞ --></mi>
            <mspace width="1em" />
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mtext>forall</mtext>
              </mrow>
            </mrow>
          </mstyle>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\displaystyle 0&lt;\int _{a}^{b}x^{2n}w(x)\,dx&lt;\infty \quad {\textrm {forall}}}}</annotation>
  </semantics>
</math>

SVG (11 KB / 4.671 KB) :

{\displaystyle {\displaystyle 0<\int _{a}^{b}x^{2n}w(x)\,dx<\infty \quad {\textrm {forall}}}}

PNG (0 B / 8 B) :


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 Orthogonal polynomials page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results