- DRMF

General

Display information for equation id:math.63461.49 on revision:63461

* Page found: Results of Parabolic Cylinder Functions (eq math.63461.49)

Occurrences on the following pages:

Results of Parabolic Cylinder Functions Eq: math.63461.49

Hash: 704a90f2496c31938ce94424b432eccd

TeX (original user input):

2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2}}\KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}} = 2^{-\frac{1}{2}a}z^{-\frac{1}{2}}\WhittakerconfhyperW{-\frac{1}{2}a}{-\frac{1}{4}}@{\tfrac{1}{2}z^{2}}

TeX (checked):

LaTeXML (experimental; uses MathML) rendering

MathML (20.497 KB / 2.552 KB) :

{\displaystyle{\displaystyle 2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2% }}U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{-% \frac{1}{2}a}z^{-\frac{1}{2}}W_{-\frac{1}{2}a,-\frac{1}{4}}\left(\tfrac{1}{2}z% ^{2}\right)}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle 2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2%&#10;}}U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{-%&#10;\frac{1}{2}a}z^{-\frac{1}{2}}W_{-\frac{1}{2}a,-\frac{1}{4}}\left(\tfrac{1}{2}z%&#10;^{2}\right)}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
      <mrow id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">
        <msup id="p1.1.m1.1.13.1.2" xref="p1.1.m1.1.13.1.2.cmml">
          <mn id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">2</mn>
          <mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
            <mrow id="p1.1.m1.1.2.1.6" xref="p1.1.m1.1.2.1.6.cmml">
              <mo id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">-</mo>
              <mfrac id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml">
                <mn id="p1.1.m1.1.2.1.2.2" xref="p1.1.m1.1.2.1.2.2.cmml">3</mn>
                <mn id="p1.1.m1.1.2.1.2.3" xref="p1.1.m1.1.2.1.2.3.cmml">4</mn>
              </mfrac>
            </mrow>
            <mo id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml">-</mo>
            <mrow id="p1.1.m1.1.2.1.7" xref="p1.1.m1.1.2.1.7.cmml">
              <mfrac id="p1.1.m1.1.2.1.4" xref="p1.1.m1.1.2.1.4.cmml">
                <mn id="p1.1.m1.1.2.1.4.2" xref="p1.1.m1.1.2.1.4.2.cmml">1</mn>
                <mn id="p1.1.m1.1.2.1.4.3" xref="p1.1.m1.1.2.1.4.3.cmml">2</mn>
              </mfrac>
              <mo id="p1.1.m1.1.2.1.7.1" xref="p1.1.m1.1.2.1.7.1.cmml">⁢</mo>
              <mi id="p1.1.m1.1.2.1.5" xref="p1.1.m1.1.2.1.5.cmml">a</mi>
            </mrow>
          </mrow>
        </msup>
        <mo id="p1.1.m1.1.13.1.1" xref="p1.1.m1.1.13.1.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">z</mi>
        <mo id="p1.1.m1.1.13.1.1a" xref="p1.1.m1.1.13.1.1.cmml">⁢</mo>
        <msup id="p1.1.m1.1.13.1.3" xref="p1.1.m1.1.13.1.3.cmml">
          <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">e</mi>
          <mrow id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">
            <mo id="p1.1.m1.1.5.1.1" xref="p1.1.m1.1.5.1.1.cmml">-</mo>
            <mrow id="p1.1.m1.1.5.1.5" xref="p1.1.m1.1.5.1.5.cmml">
              <mfrac id="p1.1.m1.1.5.1.2" xref="p1.1.m1.1.5.1.2.cmml">
                <mn id="p1.1.m1.1.5.1.2.2" xref="p1.1.m1.1.5.1.2.2.cmml">1</mn>
                <mn id="p1.1.m1.1.5.1.2.3" xref="p1.1.m1.1.5.1.2.3.cmml">4</mn>
              </mfrac>
              <mo id="p1.1.m1.1.5.1.5.1" xref="p1.1.m1.1.5.1.5.1.cmml">⁢</mo>
              <msup id="p1.1.m1.1.5.1.5.2" xref="p1.1.m1.1.5.1.5.2.cmml">
                <mi id="p1.1.m1.1.5.1.3" xref="p1.1.m1.1.5.1.3.cmml">z</mi>
                <mn id="p1.1.m1.1.5.1.4.1" xref="p1.1.m1.1.5.1.4.1.cmml">2</mn>
              </msup>
            </mrow>
          </mrow>
        </msup>
        <mo id="p1.1.m1.1.13.1.1b" xref="p1.1.m1.1.13.1.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.6.11.2" xref="p1.1.m1.1.6.1.cmml">
          <mi id="p1.1.m1.1.6.2.1.2" xref="p1.1.m1.1.6.2.1.1.cmml">U</mi>
          <mo id="p1.1.m1.1.6.11.2a" xref="p1.1.m1.1.6.1.cmml">⁡</mo>
          <mrow id="p1.1.m1.1.6.11.2.1" xref="p1.1.m1.1.6.1.cmml">
            <mo id="p1.1.m1.1.6.4" xref="p1.1.m1.1.6.1.cmml">(</mo>
            <mrow id="p1.1.m1.1.6.5" xref="p1.1.m1.1.6.5.cmml">
              <mrow id="p1.1.m1.1.6.5.5" xref="p1.1.m1.1.6.5.5.cmml">
                <mfrac id="p1.1.m1.1.6.5.1" xref="p1.1.m1.1.6.5.1.cmml">
                  <mn id="p1.1.m1.1.6.5.1.2" xref="p1.1.m1.1.6.5.1.2.cmml">1</mn>
                  <mn id="p1.1.m1.1.6.5.1.3" xref="p1.1.m1.1.6.5.1.3.cmml">2</mn>
                </mfrac>
                <mo id="p1.1.m1.1.6.5.5.1" xref="p1.1.m1.1.6.5.5.1.cmml">⁢</mo>
                <mi id="p1.1.m1.1.6.5.2" xref="p1.1.m1.1.6.5.2.cmml">a</mi>
              </mrow>
              <mo id="p1.1.m1.1.6.5.3" xref="p1.1.m1.1.6.5.3.cmml">+</mo>
              <mfrac id="p1.1.m1.1.6.5.4" xref="p1.1.m1.1.6.5.4.cmml">
                <mn id="p1.1.m1.1.6.5.4.2" xref="p1.1.m1.1.6.5.4.2.cmml">3</mn>
                <mn id="p1.1.m1.1.6.5.4.3" xref="p1.1.m1.1.6.5.4.3.cmml">4</mn>
              </mfrac>
            </mrow>
            <mo id="p1.1.m1.1.6.6" xref="p1.1.m1.1.6.1.cmml">,</mo>
            <mfrac id="p1.1.m1.1.6.7" xref="p1.1.m1.1.6.7.cmml">
              <mn id="p1.1.m1.1.6.7.1.2" xref="p1.1.m1.1.6.7.1.2.cmml">3</mn>
              <mn id="p1.1.m1.1.6.7.1.3" xref="p1.1.m1.1.6.7.1.3.cmml">2</mn>
            </mfrac>
            <mo id="p1.1.m1.1.6.8" xref="p1.1.m1.1.6.1.cmml">,</mo>
            <mrow id="p1.1.m1.1.6.9" xref="p1.1.m1.1.6.9.cmml">
              <mfrac id="p1.1.m1.1.6.9.1" xref="p1.1.m1.1.6.9.1.cmml">
                <mn id="p1.1.m1.1.6.9.1.2" xref="p1.1.m1.1.6.9.1.2.cmml">1</mn>
                <mn id="p1.1.m1.1.6.9.1.3" xref="p1.1.m1.1.6.9.1.3.cmml">2</mn>
              </mfrac>
              <mo id="p1.1.m1.1.6.9.4" xref="p1.1.m1.1.6.9.4.cmml">⁢</mo>
              <msup id="p1.1.m1.1.6.9.5" xref="p1.1.m1.1.6.9.5.cmml">
                <mi id="p1.1.m1.1.6.9.2" xref="p1.1.m1.1.6.9.2.cmml">z</mi>
                <mn id="p1.1.m1.1.6.9.3.1" xref="p1.1.m1.1.6.9.3.1.cmml">2</mn>
              </msup>
            </mrow>
            <mo id="p1.1.m1.1.6.10" xref="p1.1.m1.1.6.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
      <mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
        <msup id="p1.1.m1.1.13.2.2" xref="p1.1.m1.1.13.2.2.cmml">
          <mn id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">2</mn>
          <mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
            <mo id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml">-</mo>
            <mrow id="p1.1.m1.1.9.1.4" xref="p1.1.m1.1.9.1.4.cmml">
              <mfrac id="p1.1.m1.1.9.1.2" xref="p1.1.m1.1.9.1.2.cmml">
                <mn id="p1.1.m1.1.9.1.2.2" xref="p1.1.m1.1.9.1.2.2.cmml">1</mn>
                <mn id="p1.1.m1.1.9.1.2.3" xref="p1.1.m1.1.9.1.2.3.cmml">2</mn>
              </mfrac>
              <mo id="p1.1.m1.1.9.1.4.1" xref="p1.1.m1.1.9.1.4.1.cmml">⁢</mo>
              <mi id="p1.1.m1.1.9.1.3" xref="p1.1.m1.1.9.1.3.cmml">a</mi>
            </mrow>
          </mrow>
        </msup>
        <mo id="p1.1.m1.1.13.2.1" xref="p1.1.m1.1.13.2.1.cmml">⁢</mo>
        <msup id="p1.1.m1.1.13.2.3" xref="p1.1.m1.1.13.2.3.cmml">
          <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">z</mi>
          <mrow id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
            <mo id="p1.1.m1.1.11.1.1" xref="p1.1.m1.1.11.1.1.cmml">-</mo>
            <mfrac id="p1.1.m1.1.11.1.2" xref="p1.1.m1.1.11.1.2.cmml">
              <mn id="p1.1.m1.1.11.1.2.2" xref="p1.1.m1.1.11.1.2.2.cmml">1</mn>
              <mn id="p1.1.m1.1.11.1.2.3" xref="p1.1.m1.1.11.1.2.3.cmml">2</mn>
            </mfrac>
          </mrow>
        </msup>
        <mo id="p1.1.m1.1.13.2.1a" xref="p1.1.m1.1.13.2.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.12.7.2" xref="p1.1.m1.1.12.1.cmml">
          <msub id="p1.1.m1.1.12.2.1.4" xref="p1.1.m1.1.12.2.1.1.cmml">
            <mi id="p1.1.m1.1.12.2.1.2" xref="p1.1.m1.1.12.2.1.1.1.cmml">W</mi>
            <mrow id="p1.1.m1.1.12.2.1.3.1" xref="p1.1.m1.1.12.2.1.1.cmml">
              <mrow id="p1.1.m1.1.12.2.1.3.1.1" xref="p1.1.m1.1.12.2.1.3.1.1.cmml">
                <mo id="p1.1.m1.1.12.2.1.3.1.1.1" xref="p1.1.m1.1.12.2.1.3.1.1.1.cmml">-</mo>
                <mrow id="p1.1.m1.1.12.2.1.3.1.1.4" xref="p1.1.m1.1.12.2.1.3.1.1.4.cmml">
                  <mfrac id="p1.1.m1.1.12.2.1.3.1.1.2" xref="p1.1.m1.1.12.2.1.3.1.1.2.cmml">
                    <mn id="p1.1.m1.1.12.2.1.3.1.1.2.2" xref="p1.1.m1.1.12.2.1.3.1.1.2.2.cmml">1</mn>
                    <mn id="p1.1.m1.1.12.2.1.3.1.1.2.3" xref="p1.1.m1.1.12.2.1.3.1.1.2.3.cmml">2</mn>
                  </mfrac>
                  <mo id="p1.1.m1.1.12.2.1.3.1.1.4.1" xref="p1.1.m1.1.12.2.1.3.1.1.4.1.cmml">⁢</mo>
                  <mi id="p1.1.m1.1.12.2.1.3.1.1.3" xref="p1.1.m1.1.12.2.1.3.1.1.3.cmml">a</mi>
                </mrow>
              </mrow>
              <mo id="p1.1.m1.1.12.2.1.3.1.2" xref="p1.1.m1.1.12.2.1.1.1.cmml">,</mo>
              <mrow id="p1.1.m1.1.12.2.1.3.1.3" xref="p1.1.m1.1.12.2.1.3.1.3.cmml">
                <mo id="p1.1.m1.1.12.2.1.3.1.3.1" xref="p1.1.m1.1.12.2.1.3.1.3.1.cmml">-</mo>
                <mfrac id="p1.1.m1.1.12.2.1.3.1.3.2" xref="p1.1.m1.1.12.2.1.3.1.3.2.cmml">
                  <mn id="p1.1.m1.1.12.2.1.3.1.3.2.2" xref="p1.1.m1.1.12.2.1.3.1.3.2.2.cmml">1</mn>
                  <mn id="p1.1.m1.1.12.2.1.3.1.3.2.3" xref="p1.1.m1.1.12.2.1.3.1.3.2.3.cmml">4</mn>
                </mfrac>
              </mrow>
            </mrow>
          </msub>
          <mo id="p1.1.m1.1.12.7.2a" xref="p1.1.m1.1.12.1.cmml">⁡</mo>
          <mrow id="p1.1.m1.1.12.7.2.1" xref="p1.1.m1.1.12.1.cmml">
            <mo id="p1.1.m1.1.12.4" xref="p1.1.m1.1.12.1.cmml">(</mo>
            <mrow id="p1.1.m1.1.12.5" xref="p1.1.m1.1.12.5.cmml">
              <mfrac id="p1.1.m1.1.12.5.1" xref="p1.1.m1.1.12.5.1.cmml">
                <mn id="p1.1.m1.1.12.5.1.2" xref="p1.1.m1.1.12.5.1.2.cmml">1</mn>
                <mn id="p1.1.m1.1.12.5.1.3" xref="p1.1.m1.1.12.5.1.3.cmml">2</mn>
              </mfrac>
              <mo id="p1.1.m1.1.12.5.4" xref="p1.1.m1.1.12.5.4.cmml">⁢</mo>
              <msup id="p1.1.m1.1.12.5.5" xref="p1.1.m1.1.12.5.5.cmml">
                <mi id="p1.1.m1.1.12.5.2" xref="p1.1.m1.1.12.5.2.cmml">z</mi>
                <mn id="p1.1.m1.1.12.5.3.1" xref="p1.1.m1.1.12.5.3.1.cmml">2</mn>
              </msup>
            </mrow>
            <mo id="p1.1.m1.1.12.6" xref="p1.1.m1.1.12.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
        <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
        <apply id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">
          <times id="p1.1.m1.1.13.1.1.cmml" xref="p1.1.m1.1.13.1.1"/>
          <apply id="p1.1.m1.1.13.1.2.cmml" xref="p1.1.m1.1.13.1.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.13.1.2.1.cmml" xref="p1.1.m1.1.13.1.2">superscript</csymbol>
            <cn type="integer" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">2</cn>
            <apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
              <minus id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3"/>
              <apply id="p1.1.m1.1.2.1.6.cmml" xref="p1.1.m1.1.2.1.6">
                <minus id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1"/>
                <apply id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2">
                  <divide id="p1.1.m1.1.2.1.2.1.cmml" xref="p1.1.m1.1.2.1.2"/>
                  <cn type="integer" id="p1.1.m1.1.2.1.2.2.cmml" xref="p1.1.m1.1.2.1.2.2">3</cn>
                  <cn type="integer" id="p1.1.m1.1.2.1.2.3.cmml" xref="p1.1.m1.1.2.1.2.3">4</cn>
                </apply>
              </apply>
              <apply id="p1.1.m1.1.2.1.7.cmml" xref="p1.1.m1.1.2.1.7">
                <times id="p1.1.m1.1.2.1.7.1.cmml" xref="p1.1.m1.1.2.1.7.1"/>
                <apply id="p1.1.m1.1.2.1.4.cmml" xref="p1.1.m1.1.2.1.4">
                  <divide id="p1.1.m1.1.2.1.4.1.cmml" xref="p1.1.m1.1.2.1.4"/>
                  <cn type="integer" id="p1.1.m1.1.2.1.4.2.cmml" xref="p1.1.m1.1.2.1.4.2">1</cn>
                  <cn type="integer" id="p1.1.m1.1.2.1.4.3.cmml" xref="p1.1.m1.1.2.1.4.3">2</cn>
                </apply>
                <ci id="p1.1.m1.1.2.1.5.cmml" xref="p1.1.m1.1.2.1.5">𝑎</ci>
              </apply>
            </apply>
          </apply>
          <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑧</ci>
          <apply id="p1.1.m1.1.13.1.3.cmml" xref="p1.1.m1.1.13.1.3">
            <csymbol cd="ambiguous" id="p1.1.m1.1.13.1.3.1.cmml" xref="p1.1.m1.1.13.1.3">superscript</csymbol>
            <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝑒</ci>
            <apply id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">
              <minus id="p1.1.m1.1.5.1.1.cmml" xref="p1.1.m1.1.5.1.1"/>
              <apply id="p1.1.m1.1.5.1.5.cmml" xref="p1.1.m1.1.5.1.5">
                <times id="p1.1.m1.1.5.1.5.1.cmml" xref="p1.1.m1.1.5.1.5.1"/>
                <apply id="p1.1.m1.1.5.1.2.cmml" xref="p1.1.m1.1.5.1.2">
                  <divide id="p1.1.m1.1.5.1.2.1.cmml" xref="p1.1.m1.1.5.1.2"/>
                  <cn type="integer" id="p1.1.m1.1.5.1.2.2.cmml" xref="p1.1.m1.1.5.1.2.2">1</cn>
                  <cn type="integer" id="p1.1.m1.1.5.1.2.3.cmml" xref="p1.1.m1.1.5.1.2.3">4</cn>
                </apply>
                <apply id="p1.1.m1.1.5.1.5.2.cmml" xref="p1.1.m1.1.5.1.5.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.5.1.5.2.1.cmml" xref="p1.1.m1.1.5.1.5.2">superscript</csymbol>
                  <ci id="p1.1.m1.1.5.1.3.cmml" xref="p1.1.m1.1.5.1.3">𝑧</ci>
                  <cn type="integer" id="p1.1.m1.1.5.1.4.1.cmml" xref="p1.1.m1.1.5.1.4.1">2</cn>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.11.2">
            <csymbol cd="dlmf" id="p1.1.m1.1.6.2.1.1.cmml" xref="p1.1.m1.1.6.2.1.2">Kummer-confluent-hypergeometric-U</csymbol>
            <apply id="p1.1.m1.1.6.5.cmml" xref="p1.1.m1.1.6.5">
              <plus id="p1.1.m1.1.6.5.3.cmml" xref="p1.1.m1.1.6.5.3"/>
              <apply id="p1.1.m1.1.6.5.5.cmml" xref="p1.1.m1.1.6.5.5">
                <times id="p1.1.m1.1.6.5.5.1.cmml" xref="p1.1.m1.1.6.5.5.1"/>
                <apply id="p1.1.m1.1.6.5.1.cmml" xref="p1.1.m1.1.6.5.1">
                  <divide id="p1.1.m1.1.6.5.1.1.cmml" xref="p1.1.m1.1.6.5.1"/>
                  <cn type="integer" id="p1.1.m1.1.6.5.1.2.cmml" xref="p1.1.m1.1.6.5.1.2">1</cn>
                  <cn type="integer" id="p1.1.m1.1.6.5.1.3.cmml" xref="p1.1.m1.1.6.5.1.3">2</cn>
                </apply>
                <ci id="p1.1.m1.1.6.5.2.cmml" xref="p1.1.m1.1.6.5.2">𝑎</ci>
              </apply>
              <apply id="p1.1.m1.1.6.5.4.cmml" xref="p1.1.m1.1.6.5.4">
                <divide id="p1.1.m1.1.6.5.4.1.cmml" xref="p1.1.m1.1.6.5.4"/>
                <cn type="integer" id="p1.1.m1.1.6.5.4.2.cmml" xref="p1.1.m1.1.6.5.4.2">3</cn>
                <cn type="integer" id="p1.1.m1.1.6.5.4.3.cmml" xref="p1.1.m1.1.6.5.4.3">4</cn>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.6.7.cmml" xref="p1.1.m1.1.6.7">
              <divide id="p1.1.m1.1.6.7.1.1.cmml" xref="p1.1.m1.1.6.7"/>
              <cn type="integer" id="p1.1.m1.1.6.7.1.2.cmml" xref="p1.1.m1.1.6.7.1.2">3</cn>
              <cn type="integer" id="p1.1.m1.1.6.7.1.3.cmml" xref="p1.1.m1.1.6.7.1.3">2</cn>
            </apply>
            <apply id="p1.1.m1.1.6.9.cmml" xref="p1.1.m1.1.6.9">
              <times id="p1.1.m1.1.6.9.4.cmml" xref="p1.1.m1.1.6.9.4"/>
              <apply id="p1.1.m1.1.6.9.1.cmml" xref="p1.1.m1.1.6.9.1">
                <divide id="p1.1.m1.1.6.9.1.1.cmml" xref="p1.1.m1.1.6.9.1"/>
                <cn type="integer" id="p1.1.m1.1.6.9.1.2.cmml" xref="p1.1.m1.1.6.9.1.2">1</cn>
                <cn type="integer" id="p1.1.m1.1.6.9.1.3.cmml" xref="p1.1.m1.1.6.9.1.3">2</cn>
              </apply>
              <apply id="p1.1.m1.1.6.9.5.cmml" xref="p1.1.m1.1.6.9.5">
                <csymbol cd="ambiguous" id="p1.1.m1.1.6.9.5.1.cmml" xref="p1.1.m1.1.6.9.5">superscript</csymbol>
                <ci id="p1.1.m1.1.6.9.2.cmml" xref="p1.1.m1.1.6.9.2">𝑧</ci>
                <cn type="integer" id="p1.1.m1.1.6.9.3.1.cmml" xref="p1.1.m1.1.6.9.3.1">2</cn>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">
          <times id="p1.1.m1.1.13.2.1.cmml" xref="p1.1.m1.1.13.2.1"/>
          <apply id="p1.1.m1.1.13.2.2.cmml" xref="p1.1.m1.1.13.2.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.2.1.cmml" xref="p1.1.m1.1.13.2.2">superscript</csymbol>
            <cn type="integer" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">2</cn>
            <apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
              <minus id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1"/>
              <apply id="p1.1.m1.1.9.1.4.cmml" xref="p1.1.m1.1.9.1.4">
                <times id="p1.1.m1.1.9.1.4.1.cmml" xref="p1.1.m1.1.9.1.4.1"/>
                <apply id="p1.1.m1.1.9.1.2.cmml" xref="p1.1.m1.1.9.1.2">
                  <divide id="p1.1.m1.1.9.1.2.1.cmml" xref="p1.1.m1.1.9.1.2"/>
                  <cn type="integer" id="p1.1.m1.1.9.1.2.2.cmml" xref="p1.1.m1.1.9.1.2.2">1</cn>
                  <cn type="integer" id="p1.1.m1.1.9.1.2.3.cmml" xref="p1.1.m1.1.9.1.2.3">2</cn>
                </apply>
                <ci id="p1.1.m1.1.9.1.3.cmml" xref="p1.1.m1.1.9.1.3">𝑎</ci>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.13.2.3.cmml" xref="p1.1.m1.1.13.2.3">
            <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.3.1.cmml" xref="p1.1.m1.1.13.2.3">superscript</csymbol>
            <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑧</ci>
            <apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
              <minus id="p1.1.m1.1.11.1.1.cmml" xref="p1.1.m1.1.11.1.1"/>
              <apply id="p1.1.m1.1.11.1.2.cmml" xref="p1.1.m1.1.11.1.2">
                <divide id="p1.1.m1.1.11.1.2.1.cmml" xref="p1.1.m1.1.11.1.2"/>
                <cn type="integer" id="p1.1.m1.1.11.1.2.2.cmml" xref="p1.1.m1.1.11.1.2.2">1</cn>
                <cn type="integer" id="p1.1.m1.1.11.1.2.3.cmml" xref="p1.1.m1.1.11.1.2.3">2</cn>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.7.2">
            <apply id="p1.1.m1.1.12.2.1.1.cmml" xref="p1.1.m1.1.12.2.1.4">
              <csymbol cd="dlmf" id="p1.1.m1.1.12.2.1.1.1.cmml" xref="p1.1.m1.1.12.2.1.2">Whittaker-confluent-hypergeometric-W</csymbol>
              <apply id="p1.1.m1.1.12.2.1.3.1.1.cmml" xref="p1.1.m1.1.12.2.1.3.1.1">
                <minus id="p1.1.m1.1.12.2.1.3.1.1.1.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.1"/>
                <apply id="p1.1.m1.1.12.2.1.3.1.1.4.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.4">
                  <times id="p1.1.m1.1.12.2.1.3.1.1.4.1.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.4.1"/>
                  <apply id="p1.1.m1.1.12.2.1.3.1.1.2.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.2">
                    <divide id="p1.1.m1.1.12.2.1.3.1.1.2.1.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.2"/>
                    <cn type="integer" id="p1.1.m1.1.12.2.1.3.1.1.2.2.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.2.2">1</cn>
                    <cn type="integer" id="p1.1.m1.1.12.2.1.3.1.1.2.3.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.2.3">2</cn>
                  </apply>
                  <ci id="p1.1.m1.1.12.2.1.3.1.1.3.cmml" xref="p1.1.m1.1.12.2.1.3.1.1.3">𝑎</ci>
                </apply>
              </apply>
              <apply id="p1.1.m1.1.12.2.1.3.1.3.cmml" xref="p1.1.m1.1.12.2.1.3.1.3">
                <minus id="p1.1.m1.1.12.2.1.3.1.3.1.cmml" xref="p1.1.m1.1.12.2.1.3.1.3.1"/>
                <apply id="p1.1.m1.1.12.2.1.3.1.3.2.cmml" xref="p1.1.m1.1.12.2.1.3.1.3.2">
                  <divide id="p1.1.m1.1.12.2.1.3.1.3.2.1.cmml" xref="p1.1.m1.1.12.2.1.3.1.3.2"/>
                  <cn type="integer" id="p1.1.m1.1.12.2.1.3.1.3.2.2.cmml" xref="p1.1.m1.1.12.2.1.3.1.3.2.2">1</cn>
                  <cn type="integer" id="p1.1.m1.1.12.2.1.3.1.3.2.3.cmml" xref="p1.1.m1.1.12.2.1.3.1.3.2.3">4</cn>
                </apply>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.12.5.cmml" xref="p1.1.m1.1.12.5">
              <times id="p1.1.m1.1.12.5.4.cmml" xref="p1.1.m1.1.12.5.4"/>
              <apply id="p1.1.m1.1.12.5.1.cmml" xref="p1.1.m1.1.12.5.1">
                <divide id="p1.1.m1.1.12.5.1.1.cmml" xref="p1.1.m1.1.12.5.1"/>
                <cn type="integer" id="p1.1.m1.1.12.5.1.2.cmml" xref="p1.1.m1.1.12.5.1.2">1</cn>
                <cn type="integer" id="p1.1.m1.1.12.5.1.3.cmml" xref="p1.1.m1.1.12.5.1.3">2</cn>
              </apply>
              <apply id="p1.1.m1.1.12.5.5.cmml" xref="p1.1.m1.1.12.5.5">
                <csymbol cd="ambiguous" id="p1.1.m1.1.12.5.5.1.cmml" xref="p1.1.m1.1.12.5.5">superscript</csymbol>
                <ci id="p1.1.m1.1.12.5.2.cmml" xref="p1.1.m1.1.12.5.2">𝑧</ci>
                <cn type="integer" id="p1.1.m1.1.12.5.3.1.cmml" xref="p1.1.m1.1.12.5.3.1">2</cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle 2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2%
}}U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{-%
\frac{1}{2}a}z^{-\frac{1}{2}}W_{-\frac{1}{2}a,-\frac{1}{4}}\left(\tfrac{1}{2}z%
^{2}\right)}}</annotation>
  </semantics>
</math>

SVG (21.526 KB / 5.245 KB) :

SVG (MathML can be enabled via browser plugin) rendering

MathML (0 B / 8 B) :

Failed to get svg.

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

( ! ) Warning: Trying to access array offset on value of type null in /var/www/html/extensions/MathSearch/includes/FormulaInfo.php on line 112
Call Stack
#	Time	Memory	Function	Location
1	0.0001	354792	{main}( )	.../index.php:0
2	0.0201	1736512	wfIndexMain( )	.../index.php:46
3	0.0201	1736608	MediaWiki->run( )	.../index.php:50
4	0.0201	1736608	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0205	1749976	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0602	2009952	MediaWiki\SpecialPage\SpecialPageFactory->executePath( $path = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = TRUE; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $context = class RequestContext { private $request = class WebRequest { protected $data = [...]; protected $queryAndPathParams = [...]; protected $queryParams = [...]; protected $headers = [...]; private $response = class WebResponse { ... }; private $ip = '172.16.5.238'; protected $requestTime = 1685530141.0034; protected $protocol = 'https'; protected $sessionId = class MediaWiki\Session\SessionId { ... }; protected $markedAsSafe = FALSE }; private $title = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'Special:FormulaInfo'; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $wikipage = NULL; private $action = NULL; private $output = class OutputPage { private ${ContextSource}context = ...; protected $mMetatags = [...]; protected $mLinktags = [...]; protected $mCanonicalUrl = FALSE; private $mPageTitle = ''; private $displayTitle = NULL; private $cacheIsFinal = FALSE; public $mBodytext = '<h2><span class="mw-headline" id="General">General</span></h2><p>Display information for equation id:math.63461.49 on revision:63461\n</p><p>* Page found: <a href="/wiki/Results_of_Parabolic_Cylinder_Functions#math.63461.49" title="Results of Parabolic Cylinder Functions">Results of Parabolic Cylinder Functions</a> (eq math.63461.49) </p><a href="/index.php?title=Results_of_Parabolic_Cylinder_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a '...; private $mHTMLtitle = ''; private $mIsArticle = FALSE; private $mIsArticleRelated = TRUE; private $mHasCopyright = FALSE; private $mPrintable = FALSE; private $tocData = class Wikimedia\Parsoid\Core\TOCData { ... }; private $mSubtitle = [...]; public $mRedirect = ''; protected $mStatusCode = NULL; protected $mLastModified = ''; protected $mCategoryLinks = [...]; protected $mCategories = [...]; protected $mIndicators = [...]; private $mLanguageLinks = [...]; private $mScripts = ''; protected $mInlineStyles = ''; public $mPageLinkTitle = ''; protected $mAdditionalHtmlClasses = [...]; protected $mHeadItems = [...]; protected $mAdditionalBodyClasses = [...]; protected $mModules = [...]; protected $mModuleStyles = [...]; protected $mResourceLoader = NULL; private $rlClient = NULL; private $rlClientContext = NULL; private $rlExemptStyleModules = NULL; protected $mJsConfigVars = [...]; protected $mTemplateIds = [...]; protected $mImageTimeKeys = [...]; public $mRedirectCode = ''; protected $mFeedLinksAppendQuery = NULL; protected $mAllowedModules = [...]; protected $mDoNothing = FALSE; protected $mParserOptions = class ParserOptions { ... }; private $mFeedLinks = [...]; protected $mEnableClientCache = TRUE; private $mArticleBodyOnly = FALSE; protected $mNewSectionLink = FALSE; protected $mHideNewSectionLink = FALSE; public $mNoGallery = FALSE; protected $mCdnMaxage = 0; protected $mCdnMaxageLimit = INF; protected $mPreventClickjacking = TRUE; private $mRevisionId = NULL; private $mRevisionIsCurrent = NULL; private $mRevisionTimestamp = NULL; protected $mFileVersion = NULL; protected $styles = [...]; private $mIndexPolicy = 'index'; private $mFollowPolicy = 'follow'; private $mRobotsOptions = [...]; private $mVaryHeader = [...]; private $mRedirectedFrom = NULL; private $mProperties = [...]; private $mTarget = NULL; private $mEnableTOC = FALSE; private $copyrightUrl = NULL; private $limitReportJSData = [...]; private $contentOverrides = [...]; private $contentOverrideCallbacks = [...]; private $mLinkHeader = [...]; private $CSP = class ContentSecurityPolicy { ... } }; private $user = class User { public $mId = 0; public $mName = FALSE; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20230531104901'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = NULL; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $authority = NULL; private $lang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = 'en'; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}namespaceInfo = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}localisationCache = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langNameUtils = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langFallback = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookContainer = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookRunner = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}config = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}overrideUcfirstCharacters = NULL }; private $skin = class MediaWiki\Skins\Vector\SkinVectorLegacy { private ${ContextSource}context = ...; private ${Skin}defaultLinkOptions = [...]; protected $skinname = 'vector'; protected $options = [...]; protected $mRelevantTitle = NULL; private ${Skin}mRelevantUser = FALSE; private ${Skin}languageLinks = NULL; private ${Skin}sidebar = NULL; private ${Skin}componentRegistry = class MediaWiki\Skin\SkinComponentRegistry { ... }; public $template = NULL; public $thispage = NULL; public $titletxt = NULL; public $userpage = NULL; public $thisquery = NULL; public $loggedin = NULL; public $username = NULL; public $userpageUrlDetails = NULL; private ${SkinTemplate}isTempUser = NULL; private ${SkinTemplate}isNamedUser = NULL; private ${SkinTemplate}templateContextSet = FALSE; private ${SkinTemplate}contentNavigationCached = NULL; private ${SkinMustache}templateParser = NULL; private ${MediaWiki\Skins\Vector\SkinVector}languages = NULL }; private $timing = NULL; private $config = class GlobalVarConfig { private $prefix = 'wg' }; private $languageRecursion = FALSE }, $including = ???, $linkRenderer = ??? )	.../MediaWiki.php:324
7	0.0604	2013856	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0604	2013856	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0604	2013856	FormulaInfo->DisplayInfo( $oldID = '63461', $eid = 'math.63461.49' )	.../FormulaInfo.php:45
10	0.9097	5274512	FormulaInfo::DisplayTranslations( $tex = '2^{-\\frac{3}{4}-\\frac{1}{2}a}ze^{-\\frac{1}{4}z^{2}}\\KummerconfhyperU@{\\tfrac{1}{2}a+\\tfrac{3}{4}}{\\tfrac{3}{2}}{\\tfrac{1}{2}z^{2}} = 2^{-\\frac{1}{2}a}z^{-\\frac{1}{2}}\\WhittakerconfhyperW{-\\frac{1}{2}a}{-\\frac{1}{4}}@{\\tfrac{1}{2}z^{2}}' )	.../FormulaInfo.php:168
11	0.9244	5322264	FormulaInfo::PrintTranslationResult( $cas = 'Maple', $result = '<html>\r\n<head><title>301 Moved Permanently</title></head>\r\n<body>\r\n<center><h1>301 Moved Permanently</h1></center>\r\n<hr><center>nginx/1.18.0</center>\r\n</body>\r\n</html>\r\n' )	.../FormulaInfo.php:90

( ! ) Warning: Trying to access array offset on value of type null in /var/www/html/extensions/MathSearch/includes/FormulaInfo.php on line 115
Call Stack
#	Time	Memory	Function	Location
1	0.0001	354792	{main}( )	.../index.php:0
2	0.0201	1736512	wfIndexMain( )	.../index.php:46
3	0.0201	1736608	MediaWiki->run( )	.../index.php:50
4	0.0201	1736608	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0205	1749976	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0602	2009952	MediaWiki\SpecialPage\SpecialPageFactory->executePath( $path = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = TRUE; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $context = class RequestContext { private $request = class WebRequest { protected $data = [...]; protected $queryAndPathParams = [...]; protected $queryParams = [...]; protected $headers = [...]; private $response = class WebResponse { ... }; private $ip = '172.16.5.238'; protected $requestTime = 1685530141.0034; protected $protocol = 'https'; protected $sessionId = class MediaWiki\Session\SessionId { ... }; protected $markedAsSafe = FALSE }; private $title = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'Special:FormulaInfo'; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $wikipage = NULL; private $action = NULL; private $output = class OutputPage { private ${ContextSource}context = ...; protected $mMetatags = [...]; protected $mLinktags = [...]; protected $mCanonicalUrl = FALSE; private $mPageTitle = ''; private $displayTitle = NULL; private $cacheIsFinal = FALSE; public $mBodytext = '<h2><span class="mw-headline" id="General">General</span></h2><p>Display information for equation id:math.63461.49 on revision:63461\n</p><p>* Page found: <a href="/wiki/Results_of_Parabolic_Cylinder_Functions#math.63461.49" title="Results of Parabolic Cylinder Functions">Results of Parabolic Cylinder Functions</a> (eq math.63461.49) </p><a href="/index.php?title=Results_of_Parabolic_Cylinder_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a '...; private $mHTMLtitle = ''; private $mIsArticle = FALSE; private $mIsArticleRelated = TRUE; private $mHasCopyright = FALSE; private $mPrintable = FALSE; private $tocData = class Wikimedia\Parsoid\Core\TOCData { ... }; private $mSubtitle = [...]; public $mRedirect = ''; protected $mStatusCode = NULL; protected $mLastModified = ''; protected $mCategoryLinks = [...]; protected $mCategories = [...]; protected $mIndicators = [...]; private $mLanguageLinks = [...]; private $mScripts = ''; protected $mInlineStyles = ''; public $mPageLinkTitle = ''; protected $mAdditionalHtmlClasses = [...]; protected $mHeadItems = [...]; protected $mAdditionalBodyClasses = [...]; protected $mModules = [...]; protected $mModuleStyles = [...]; protected $mResourceLoader = NULL; private $rlClient = NULL; private $rlClientContext = NULL; private $rlExemptStyleModules = NULL; protected $mJsConfigVars = [...]; protected $mTemplateIds = [...]; protected $mImageTimeKeys = [...]; public $mRedirectCode = ''; protected $mFeedLinksAppendQuery = NULL; protected $mAllowedModules = [...]; protected $mDoNothing = FALSE; protected $mParserOptions = class ParserOptions { ... }; private $mFeedLinks = [...]; protected $mEnableClientCache = TRUE; private $mArticleBodyOnly = FALSE; protected $mNewSectionLink = FALSE; protected $mHideNewSectionLink = FALSE; public $mNoGallery = FALSE; protected $mCdnMaxage = 0; protected $mCdnMaxageLimit = INF; protected $mPreventClickjacking = TRUE; private $mRevisionId = NULL; private $mRevisionIsCurrent = NULL; private $mRevisionTimestamp = NULL; protected $mFileVersion = NULL; protected $styles = [...]; private $mIndexPolicy = 'index'; private $mFollowPolicy = 'follow'; private $mRobotsOptions = [...]; private $mVaryHeader = [...]; private $mRedirectedFrom = NULL; private $mProperties = [...]; private $mTarget = NULL; private $mEnableTOC = FALSE; private $copyrightUrl = NULL; private $limitReportJSData = [...]; private $contentOverrides = [...]; private $contentOverrideCallbacks = [...]; private $mLinkHeader = [...]; private $CSP = class ContentSecurityPolicy { ... } }; private $user = class User { public $mId = 0; public $mName = FALSE; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20230531104901'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = NULL; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $authority = NULL; private $lang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = 'en'; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}namespaceInfo = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}localisationCache = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langNameUtils = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langFallback = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookContainer = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookRunner = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}config = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}overrideUcfirstCharacters = NULL }; private $skin = class MediaWiki\Skins\Vector\SkinVectorLegacy { private ${ContextSource}context = ...; private ${Skin}defaultLinkOptions = [...]; protected $skinname = 'vector'; protected $options = [...]; protected $mRelevantTitle = NULL; private ${Skin}mRelevantUser = FALSE; private ${Skin}languageLinks = NULL; private ${Skin}sidebar = NULL; private ${Skin}componentRegistry = class MediaWiki\Skin\SkinComponentRegistry { ... }; public $template = NULL; public $thispage = NULL; public $titletxt = NULL; public $userpage = NULL; public $thisquery = NULL; public $loggedin = NULL; public $username = NULL; public $userpageUrlDetails = NULL; private ${SkinTemplate}isTempUser = NULL; private ${SkinTemplate}isNamedUser = NULL; private ${SkinTemplate}templateContextSet = FALSE; private ${SkinTemplate}contentNavigationCached = NULL; private ${SkinMustache}templateParser = NULL; private ${MediaWiki\Skins\Vector\SkinVector}languages = NULL }; private $timing = NULL; private $config = class GlobalVarConfig { private $prefix = 'wg' }; private $languageRecursion = FALSE }, $including = ???, $linkRenderer = ??? )	.../MediaWiki.php:324
7	0.0604	2013856	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0604	2013856	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0604	2013856	FormulaInfo->DisplayInfo( $oldID = '63461', $eid = 'math.63461.49' )	.../FormulaInfo.php:45
10	0.9097	5274512	FormulaInfo::DisplayTranslations( $tex = '2^{-\\frac{3}{4}-\\frac{1}{2}a}ze^{-\\frac{1}{4}z^{2}}\\KummerconfhyperU@{\\tfrac{1}{2}a+\\tfrac{3}{4}}{\\tfrac{3}{2}}{\\tfrac{1}{2}z^{2}} = 2^{-\\frac{1}{2}a}z^{-\\frac{1}{2}}\\WhittakerconfhyperW{-\\frac{1}{2}a}{-\\frac{1}{4}}@{\\tfrac{1}{2}z^{2}}' )	.../FormulaInfo.php:168
11	0.9244	5322264	FormulaInfo::PrintTranslationResult( $cas = 'Maple', $result = '<html>\r\n<head><title>301 Moved Permanently</title></head>\r\n<body>\r\n<center><h1>301 Moved Permanently</h1></center>\r\n<hr><center>nginx/1.18.0</center>\r\n</body>\r\n</html>\r\n' )	.../FormulaInfo.php:90

( ! ) Deprecated: str_replace(): Passing null to parameter #3 ($subject) of type array\|string is deprecated in /var/www/html/extensions/MathSearch/includes/FormulaInfo.php on line 115
Call Stack
#	Time	Memory	Function	Location
1	0.0001	354792	{main}( )	.../index.php:0
2	0.0201	1736512	wfIndexMain( )	.../index.php:46
3	0.0201	1736608	MediaWiki->run( )	.../index.php:50
4	0.0201	1736608	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0205	1749976	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0602	2009952	MediaWiki\SpecialPage\SpecialPageFactory->executePath( $path = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = TRUE; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $context = class RequestContext { private $request = class WebRequest { protected $data = [...]; protected $queryAndPathParams = [...]; protected $queryParams = [...]; protected $headers = [...]; private $response = class WebResponse { ... }; private $ip = '172.16.5.238'; protected $requestTime = 1685530141.0034; protected $protocol = 'https'; protected $sessionId = class MediaWiki\Session\SessionId { ... }; protected $markedAsSafe = FALSE }; private $title = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'Special:FormulaInfo'; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $wikipage = NULL; private $action = NULL; private $output = class OutputPage { private ${ContextSource}context = ...; protected $mMetatags = [...]; protected $mLinktags = [...]; protected $mCanonicalUrl = FALSE; private $mPageTitle = ''; private $displayTitle = NULL; private $cacheIsFinal = FALSE; public $mBodytext = '<h2><span class="mw-headline" id="General">General</span></h2><p>Display information for equation id:math.63461.49 on revision:63461\n</p><p>* Page found: <a href="/wiki/Results_of_Parabolic_Cylinder_Functions#math.63461.49" title="Results of Parabolic Cylinder Functions">Results of Parabolic Cylinder Functions</a> (eq math.63461.49) </p><a href="/index.php?title=Results_of_Parabolic_Cylinder_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a '...; private $mHTMLtitle = ''; private $mIsArticle = FALSE; private $mIsArticleRelated = TRUE; private $mHasCopyright = FALSE; private $mPrintable = FALSE; private $tocData = class Wikimedia\Parsoid\Core\TOCData { ... }; private $mSubtitle = [...]; public $mRedirect = ''; protected $mStatusCode = NULL; protected $mLastModified = ''; protected $mCategoryLinks = [...]; protected $mCategories = [...]; protected $mIndicators = [...]; private $mLanguageLinks = [...]; private $mScripts = ''; protected $mInlineStyles = ''; public $mPageLinkTitle = ''; protected $mAdditionalHtmlClasses = [...]; protected $mHeadItems = [...]; protected $mAdditionalBodyClasses = [...]; protected $mModules = [...]; protected $mModuleStyles = [...]; protected $mResourceLoader = NULL; private $rlClient = NULL; private $rlClientContext = NULL; private $rlExemptStyleModules = NULL; protected $mJsConfigVars = [...]; protected $mTemplateIds = [...]; protected $mImageTimeKeys = [...]; public $mRedirectCode = ''; protected $mFeedLinksAppendQuery = NULL; protected $mAllowedModules = [...]; protected $mDoNothing = FALSE; protected $mParserOptions = class ParserOptions { ... }; private $mFeedLinks = [...]; protected $mEnableClientCache = TRUE; private $mArticleBodyOnly = FALSE; protected $mNewSectionLink = FALSE; protected $mHideNewSectionLink = FALSE; public $mNoGallery = FALSE; protected $mCdnMaxage = 0; protected $mCdnMaxageLimit = INF; protected $mPreventClickjacking = TRUE; private $mRevisionId = NULL; private $mRevisionIsCurrent = NULL; private $mRevisionTimestamp = NULL; protected $mFileVersion = NULL; protected $styles = [...]; private $mIndexPolicy = 'index'; private $mFollowPolicy = 'follow'; private $mRobotsOptions = [...]; private $mVaryHeader = [...]; private $mRedirectedFrom = NULL; private $mProperties = [...]; private $mTarget = NULL; private $mEnableTOC = FALSE; private $copyrightUrl = NULL; private $limitReportJSData = [...]; private $contentOverrides = [...]; private $contentOverrideCallbacks = [...]; private $mLinkHeader = [...]; private $CSP = class ContentSecurityPolicy { ... } }; private $user = class User { public $mId = 0; public $mName = FALSE; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20230531104901'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = NULL; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $authority = NULL; private $lang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = 'en'; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}namespaceInfo = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}localisationCache = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langNameUtils = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langFallback = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookContainer = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookRunner = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}config = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}overrideUcfirstCharacters = NULL }; private $skin = class MediaWiki\Skins\Vector\SkinVectorLegacy { private ${ContextSource}context = ...; private ${Skin}defaultLinkOptions = [...]; protected $skinname = 'vector'; protected $options = [...]; protected $mRelevantTitle = NULL; private ${Skin}mRelevantUser = FALSE; private ${Skin}languageLinks = NULL; private ${Skin}sidebar = NULL; private ${Skin}componentRegistry = class MediaWiki\Skin\SkinComponentRegistry { ... }; public $template = NULL; public $thispage = NULL; public $titletxt = NULL; public $userpage = NULL; public $thisquery = NULL; public $loggedin = NULL; public $username = NULL; public $userpageUrlDetails = NULL; private ${SkinTemplate}isTempUser = NULL; private ${SkinTemplate}isNamedUser = NULL; private ${SkinTemplate}templateContextSet = FALSE; private ${SkinTemplate}contentNavigationCached = NULL; private ${SkinMustache}templateParser = NULL; private ${MediaWiki\Skins\Vector\SkinVector}languages = NULL }; private $timing = NULL; private $config = class GlobalVarConfig { private $prefix = 'wg' }; private $languageRecursion = FALSE }, $including = ???, $linkRenderer = ??? )	.../MediaWiki.php:324
7	0.0604	2013856	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0604	2013856	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0604	2013856	FormulaInfo->DisplayInfo( $oldID = '63461', $eid = 'math.63461.49' )	.../FormulaInfo.php:45
10	0.9097	5274512	FormulaInfo::DisplayTranslations( $tex = '2^{-\\frac{3}{4}-\\frac{1}{2}a}ze^{-\\frac{1}{4}z^{2}}\\KummerconfhyperU@{\\tfrac{1}{2}a+\\tfrac{3}{4}}{\\tfrac{3}{2}}{\\tfrac{1}{2}z^{2}} = 2^{-\\frac{1}{2}a}z^{-\\frac{1}{2}}\\WhittakerconfhyperW{-\\frac{1}{2}a}{-\\frac{1}{4}}@{\\tfrac{1}{2}z^{2}}' )	.../FormulaInfo.php:168
11	0.9244	5322264	FormulaInfo::PrintTranslationResult( $cas = 'Maple', $result = '<html>\r\n<head><title>301 Moved Permanently</title></head>\r\n<body>\r\n<center><h1>301 Moved Permanently</h1></center>\r\n<hr><center>nginx/1.18.0</center>\r\n</body>\r\n</html>\r\n' )	.../FormulaInfo.php:90
12	0.9285	5341624	str_replace( $search = '\n', $replace = '\n\n', $subject = NULL )	.../FormulaInfo.php:115

( ! ) Warning: Trying to access array offset on value of type null in /var/www/html/extensions/MathSearch/includes/FormulaInfo.php on line 112
Call Stack
#	Time	Memory	Function	Location
1	0.0001	354792	{main}( )	.../index.php:0
2	0.0201	1736512	wfIndexMain( )	.../index.php:46
3	0.0201	1736608	MediaWiki->run( )	.../index.php:50
4	0.0201	1736608	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0205	1749976	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0602	2009952	MediaWiki\SpecialPage\SpecialPageFactory->executePath( $path = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = TRUE; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $context = class RequestContext { private $request = class WebRequest { protected $data = [...]; protected $queryAndPathParams = [...]; protected $queryParams = [...]; protected $headers = [...]; private $response = class WebResponse { ... }; private $ip = '172.16.5.238'; protected $requestTime = 1685530141.0034; protected $protocol = 'https'; protected $sessionId = class MediaWiki\Session\SessionId { ... }; protected $markedAsSafe = FALSE }; private $title = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'Special:FormulaInfo'; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $wikipage = NULL; private $action = NULL; private $output = class OutputPage { private ${ContextSource}context = ...; protected $mMetatags = [...]; protected $mLinktags = [...]; protected $mCanonicalUrl = FALSE; private $mPageTitle = ''; private $displayTitle = NULL; private $cacheIsFinal = FALSE; public $mBodytext = '<h2><span class="mw-headline" id="General">General</span></h2><p>Display information for equation id:math.63461.49 on revision:63461\n</p><p>* Page found: <a href="/wiki/Results_of_Parabolic_Cylinder_Functions#math.63461.49" title="Results of Parabolic Cylinder Functions">Results of Parabolic Cylinder Functions</a> (eq math.63461.49) </p><a href="/index.php?title=Results_of_Parabolic_Cylinder_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a '...; private $mHTMLtitle = ''; private $mIsArticle = FALSE; private $mIsArticleRelated = TRUE; private $mHasCopyright = FALSE; private $mPrintable = FALSE; private $tocData = class Wikimedia\Parsoid\Core\TOCData { ... }; private $mSubtitle = [...]; public $mRedirect = ''; protected $mStatusCode = NULL; protected $mLastModified = ''; protected $mCategoryLinks = [...]; protected $mCategories = [...]; protected $mIndicators = [...]; private $mLanguageLinks = [...]; private $mScripts = ''; protected $mInlineStyles = ''; public $mPageLinkTitle = ''; protected $mAdditionalHtmlClasses = [...]; protected $mHeadItems = [...]; protected $mAdditionalBodyClasses = [...]; protected $mModules = [...]; protected $mModuleStyles = [...]; protected $mResourceLoader = NULL; private $rlClient = NULL; private $rlClientContext = NULL; private $rlExemptStyleModules = NULL; protected $mJsConfigVars = [...]; protected $mTemplateIds = [...]; protected $mImageTimeKeys = [...]; public $mRedirectCode = ''; protected $mFeedLinksAppendQuery = NULL; protected $mAllowedModules = [...]; protected $mDoNothing = FALSE; protected $mParserOptions = class ParserOptions { ... }; private $mFeedLinks = [...]; protected $mEnableClientCache = TRUE; private $mArticleBodyOnly = FALSE; protected $mNewSectionLink = FALSE; protected $mHideNewSectionLink = FALSE; public $mNoGallery = FALSE; protected $mCdnMaxage = 0; protected $mCdnMaxageLimit = INF; protected $mPreventClickjacking = TRUE; private $mRevisionId = NULL; private $mRevisionIsCurrent = NULL; private $mRevisionTimestamp = NULL; protected $mFileVersion = NULL; protected $styles = [...]; private $mIndexPolicy = 'index'; private $mFollowPolicy = 'follow'; private $mRobotsOptions = [...]; private $mVaryHeader = [...]; private $mRedirectedFrom = NULL; private $mProperties = [...]; private $mTarget = NULL; private $mEnableTOC = FALSE; private $copyrightUrl = NULL; private $limitReportJSData = [...]; private $contentOverrides = [...]; private $contentOverrideCallbacks = [...]; private $mLinkHeader = [...]; private $CSP = class ContentSecurityPolicy { ... } }; private $user = class User { public $mId = 0; public $mName = FALSE; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20230531104901'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = NULL; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $authority = NULL; private $lang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = 'en'; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}namespaceInfo = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}localisationCache = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langNameUtils = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langFallback = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookContainer = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookRunner = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}config = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}overrideUcfirstCharacters = NULL }; private $skin = class MediaWiki\Skins\Vector\SkinVectorLegacy { private ${ContextSource}context = ...; private ${Skin}defaultLinkOptions = [...]; protected $skinname = 'vector'; protected $options = [...]; protected $mRelevantTitle = NULL; private ${Skin}mRelevantUser = FALSE; private ${Skin}languageLinks = NULL; private ${Skin}sidebar = NULL; private ${Skin}componentRegistry = class MediaWiki\Skin\SkinComponentRegistry { ... }; public $template = NULL; public $thispage = NULL; public $titletxt = NULL; public $userpage = NULL; public $thisquery = NULL; public $loggedin = NULL; public $username = NULL; public $userpageUrlDetails = NULL; private ${SkinTemplate}isTempUser = NULL; private ${SkinTemplate}isNamedUser = NULL; private ${SkinTemplate}templateContextSet = FALSE; private ${SkinTemplate}contentNavigationCached = NULL; private ${SkinMustache}templateParser = NULL; private ${MediaWiki\Skins\Vector\SkinVector}languages = NULL }; private $timing = NULL; private $config = class GlobalVarConfig { private $prefix = 'wg' }; private $languageRecursion = FALSE }, $including = ???, $linkRenderer = ??? )	.../MediaWiki.php:324
7	0.0604	2013856	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0604	2013856	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0604	2013856	FormulaInfo->DisplayInfo( $oldID = '63461', $eid = 'math.63461.49' )	.../FormulaInfo.php:45
10	0.9097	5274512	FormulaInfo::DisplayTranslations( $tex = '2^{-\\frac{3}{4}-\\frac{1}{2}a}ze^{-\\frac{1}{4}z^{2}}\\KummerconfhyperU@{\\tfrac{1}{2}a+\\tfrac{3}{4}}{\\tfrac{3}{2}}{\\tfrac{1}{2}z^{2}} = 2^{-\\frac{1}{2}a}z^{-\\frac{1}{2}}\\WhittakerconfhyperW{-\\frac{1}{2}a}{-\\frac{1}{4}}@{\\tfrac{1}{2}z^{2}}' )	.../FormulaInfo.php:168
11	0.9294	5358968	FormulaInfo::PrintTranslationResult( $cas = 'Mathematica', $result = '<html>\r\n<head><title>301 Moved Permanently</title></head>\r\n<body>\r\n<center><h1>301 Moved Permanently</h1></center>\r\n<hr><center>nginx/1.18.0</center>\r\n</body>\r\n</html>\r\n' )	.../FormulaInfo.php:91

( ! ) Warning: Trying to access array offset on value of type null in /var/www/html/extensions/MathSearch/includes/FormulaInfo.php on line 115
Call Stack
#	Time	Memory	Function	Location
1	0.0001	354792	{main}( )	.../index.php:0
2	0.0201	1736512	wfIndexMain( )	.../index.php:46
3	0.0201	1736608	MediaWiki->run( )	.../index.php:50
4	0.0201	1736608	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0205	1749976	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0602	2009952	MediaWiki\SpecialPage\SpecialPageFactory->executePath( $path = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = TRUE; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $context = class RequestContext { private $request = class WebRequest { protected $data = [...]; protected $queryAndPathParams = [...]; protected $queryParams = [...]; protected $headers = [...]; private $response = class WebResponse { ... }; private $ip = '172.16.5.238'; protected $requestTime = 1685530141.0034; protected $protocol = 'https'; protected $sessionId = class MediaWiki\Session\SessionId { ... }; protected $markedAsSafe = FALSE }; private $title = class Title { private $mTextform = 'FormulaInfo'; private $mUrlform = 'FormulaInfo'; private $mDbkeyform = 'FormulaInfo'; private $mNamespace = -1; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 0; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'Special:FormulaInfo'; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $wikipage = NULL; private $action = NULL; private $output = class OutputPage { private ${ContextSource}context = ...; protected $mMetatags = [...]; protected $mLinktags = [...]; protected $mCanonicalUrl = FALSE; private $mPageTitle = ''; private $displayTitle = NULL; private $cacheIsFinal = FALSE; public $mBodytext = '<h2><span class="mw-headline" id="General">General</span></h2><p>Display information for equation id:math.63461.49 on revision:63461\n</p><p>* Page found: <a href="/wiki/Results_of_Parabolic_Cylinder_Functions#math.63461.49" title="Results of Parabolic Cylinder Functions">Results of Parabolic Cylinder Functions</a> (eq math.63461.49) </p><a href="/index.php?title=Results_of_Parabolic_Cylinder_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a '...; private $mHTMLtitle = ''; private $mIsArticle = FALSE; private $mIsArticleRelated = TRUE; private $mHasCopyright = FALSE; private $mPrintable = FALSE; private $tocData = class Wikimedia\Parsoid\Core\TOCData { ... }; private $mSubtitle = [...]; public $mRedirect = ''; protected $mStatusCode = NULL; protected $mLastModified = ''; protected $mCategoryLinks = [...]; protected $mCategories = [...]; protected $mIndicators = [...]; private $mLanguageLinks = [...]; private $mScripts = ''; protected $mInlineStyles = ''; public $mPageLinkTitle = ''; protected $mAdditionalHtmlClasses = [...]; protected $mHeadItems = [...]; protected $mAdditionalBodyClasses = [...]; protected $mModules = [...]; protected $mModuleStyles = [...]; protected $mResourceLoader = NULL; private $rlClient = NULL; private $rlClientContext = NULL; private $rlExemptStyleModules = NULL; protected $mJsConfigVars = [...]; protected $mTemplateIds = [...]; protected $mImageTimeKeys = [...]; public $mRedirectCode = ''; protected $mFeedLinksAppendQuery = NULL; protected $mAllowedModules = [...]; protected $mDoNothing = FALSE; protected $mParserOptions = class ParserOptions { ... }; private $mFeedLinks = [...]; protected $mEnableClientCache = TRUE; private $mArticleBodyOnly = FALSE; protected $mNewSectionLink = FALSE; protected $mHideNewSectionLink = FALSE; public $mNoGallery = FALSE; protected $mCdnMaxage = 0; protected $mCdnMaxageLimit = INF; protected $mPreventClickjacking = TRUE; private $mRevisionId = NULL; private $mRevisionIsCurrent = NULL; private $mRevisionTimestamp = NULL; protected $mFileVersion = NULL; protected $styles = [...]; private $mIndexPolicy = 'index'; private $mFollowPolicy = 'follow'; private $mRobotsOptions = [...]; private $mVaryHeader = [...]; private $mRedirectedFrom = NULL; private $mProperties = [...]; private $mTarget = NULL; private $mEnableTOC = FALSE; private $copyrightUrl = NULL; private $limitReportJSData = [...]; private $contentOverrides = [...]; private $contentOverrideCallbacks = [...]; private $mLinkHeader = [...]; private $CSP = class ContentSecurityPolicy { ... } }; private $user = class User { public $mId = 0; public $mName = FALSE; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20230531104901'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = NULL; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $authority = NULL; private $lang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = 'en'; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}namespaceInfo = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}localisationCache = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langNameUtils = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}langFallback = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookContainer = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}hookRunner = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}config = class Wikimedia\DebugInfo\Placeholder { ... }; private ${Language}overrideUcfirstCharacters = NULL }; private $skin = class MediaWiki\Skins\Vector\SkinVectorLegacy { private ${ContextSource}context = ...; private ${Skin}defaultLinkOptions = [...]; protected $skinname = 'vector'; protected $options = [...]; protected $mRelevantTitle = NULL; private ${Skin}mRelevantUser = FALSE; private ${Skin}languageLinks = NULL; private ${Skin}sidebar = NULL; private ${Skin}componentRegistry = class MediaWiki\Skin\SkinComponentRegistry { ... }; public $template = NULL; public $thispage = NULL; public $titletxt = NULL; public $userpage = NULL; public $thisquery = NULL; public $loggedin = NULL; public $username = NULL; public $userpageUrlDetails = NULL; private ${SkinTemplate}isTempUser = NULL; private ${SkinTemplate}isNamedUser = NULL; private ${SkinTemplate}templateContextSet = FALSE; private ${SkinTemplate}contentNavigationCached = NULL; private ${SkinMustache}templateParser = NULL; private ${MediaWiki\Skins\Vector\SkinVector}languages = NULL }; private $timing = NULL; private $config = class GlobalVarConfig { private $prefix = 'wg' }; private $languageRecursion = FALSE }, $including = ???, $linkRenderer = ??? )	.../MediaWiki.php:324
7	0.0604	2013856	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0604	2013856	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0604	2013856	FormulaInfo->DisplayInfo( $oldID = '63461', $eid = 'math.63461.49' )	.../FormulaInfo.php:45
10	0.9097	5274512	FormulaInfo::DisplayTranslations( $tex = '2^{-\\frac{3}{4}-\\frac{1}{2}a}ze^{-\\frac{1}{4}z^{2}}\\KummerconfhyperU@{\\tfrac{1}{2}a+\\tfrac{3}{4}}{\\tfrac{3}{2}}{\\tfrac{1}{2}z^{2}} = 2^{-\\frac{1}{2}a}z^{-\\frac{1}{2}}\\WhittakerconfhyperW{-\\frac{1}{2}a}{-\\frac{1}{4}}@{\\tfrac{1}{2}z^{2}}' )	.../FormulaInfo.php:168
11	0.9294	5358968	FormulaInfo::PrintTranslationResult( $cas = 'Mathematica', $result = '<html>\r\n<head><title>301 Moved Permanently</title></head>\r\n<body>\r\n<center><h1>301 Moved Permanently</h1></center>\r\n<hr><center>nginx/1.18.0</center>\r\n</body>\r\n</html>\r\n' )	.../FormulaInfo.php:91

General

LaTeXML (experimental; uses MathML) rendering

SVG (MathML can be enabled via browser plugin) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

SVG (MathML can be enabled via browser plugin) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search