- DRMF

General

Display information for equation id:math.63458.32 on revision:63458

* Page found: Results of Airy and Related Functions (eq math.63458.32)

Occurrences on the following pages:

Results of Airy and Related Functions Eq: math.63458.32

Hash: 8efba9907557bfaa7826c20535d18a97

TeX (original user input):

\tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}\HankelH{2}{1/3}@{\zeta e^{-\pi i/2}} = \tfrac{1}{2}\sqrt{z/3}e^{-\pi i/3}\HankelH{2}{-1/3}@{\zeta e^{-\pi i/2}}

TeX (checked):

LaTeXML (experimental; uses MathML) rendering

MathML (18.091 KB / 2.312 KB) :

{\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}{H^{(2)}_{1/3}}% \left(\zeta e^{-\pi i/2}\right)=\tfrac{1}{2}\sqrt{z/3}e^{-\pi i/3}{H^{(2)}_{-1% /3}}\left(\zeta e^{-\pi i/2}\right)}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}{H^{(2)}_{1/3}}%&#10;\left(\zeta e^{-\pi i/2}\right)=\tfrac{1}{2}\sqrt{z/3}e^{-\pi i/3}{H^{(2)}_{-1%&#10;/3}}\left(\zeta e^{-\pi i/2}\right)}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
      <mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
        <mfrac id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
          <mn id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">1</mn>
          <mn id="p1.1.m1.1.1.3" xref="p1.1.m1.1.1.3.cmml">2</mn>
        </mfrac>
        <mo id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.12.1.1.cmml">⁢</mo>
        <msqrt id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
          <mrow id="p1.1.m1.1.2.2" xref="p1.1.m1.1.2.2.cmml">
            <mi id="p1.1.m1.1.2.2.1" xref="p1.1.m1.1.2.2.1.cmml">z</mi>
            <mo id="p1.1.m1.1.2.2.2" xref="p1.1.m1.1.2.2.2.cmml">/</mo>
            <mn id="p1.1.m1.1.2.2.3" xref="p1.1.m1.1.2.2.3.cmml">3</mn>
          </mrow>
        </msqrt>
        <mo id="p1.1.m1.1.12.1.1a" xref="p1.1.m1.1.12.1.1.cmml">⁢</mo>
        <msup id="p1.1.m1.1.12.1.2" xref="p1.1.m1.1.12.1.2.cmml">
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">e</mi>
          <mrow id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">
            <mo id="p1.1.m1.1.4.1.1" xref="p1.1.m1.1.4.1.1.cmml">-</mo>
            <mrow id="p1.1.m1.1.4.1.7" xref="p1.1.m1.1.4.1.7.cmml">
              <mrow id="p1.1.m1.1.4.1.7.1" xref="p1.1.m1.1.4.1.7.1.cmml">
                <mn id="p1.1.m1.1.4.1.2" xref="p1.1.m1.1.4.1.2.cmml">2</mn>
                <mo id="p1.1.m1.1.4.1.7.1.1" xref="p1.1.m1.1.4.1.7.1.1.cmml">⁢</mo>
                <mi id="p1.1.m1.1.4.1.3" xref="p1.1.m1.1.4.1.3.cmml">π</mi>
                <mo id="p1.1.m1.1.4.1.7.1.1a" xref="p1.1.m1.1.4.1.7.1.1.cmml">⁢</mo>
                <mi id="p1.1.m1.1.4.1.4" xref="p1.1.m1.1.4.1.4.cmml">i</mi>
              </mrow>
              <mo id="p1.1.m1.1.4.1.5" xref="p1.1.m1.1.4.1.5.cmml">/</mo>
              <mn id="p1.1.m1.1.4.1.6" xref="p1.1.m1.1.4.1.6.cmml">3</mn>
            </mrow>
          </mrow>
        </msup>
        <mo id="p1.1.m1.1.12.1.1b" xref="p1.1.m1.1.12.1.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.5.7.2" xref="p1.1.m1.1.5.1.cmml">
          <msubsup id="p1.1.m1.1.5.2.1.5" xref="p1.1.m1.1.5.2.1.1.cmml">
            <mi id="p1.1.m1.1.5.2.1.2" xref="p1.1.m1.1.5.2.1.1.1.cmml">H</mi>
            <mrow id="p1.1.m1.1.5.2.1.4.1" xref="p1.1.m1.1.5.2.1.4.1.cmml">
              <mn id="p1.1.m1.1.5.2.1.4.1.1.1" xref="p1.1.m1.1.5.2.1.4.1.1.1.cmml">1</mn>
              <mo id="p1.1.m1.1.5.2.1.4.1.1.2" xref="p1.1.m1.1.5.2.1.4.1.1.2.cmml">/</mo>
              <mn id="p1.1.m1.1.5.2.1.4.1.1.3" xref="p1.1.m1.1.5.2.1.4.1.1.3.cmml">3</mn>
            </mrow>
            <mrow id="p1.1.m1.1.5.2.1.3.1" xref="p1.1.m1.1.5.2.1.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.5.2.1.3.1.1" xref="p1.1.m1.1.5.2.1.1.1.cmml">(</mo>
              <mn id="p1.1.m1.1.5.2.1.3.1.2" xref="p1.1.m1.1.5.2.1.1.1.cmml">2</mn>
              <mo stretchy="false" id="p1.1.m1.1.5.2.1.3.1.3" xref="p1.1.m1.1.5.2.1.1.1.cmml">)</mo>
            </mrow>
          </msubsup>
          <mo id="p1.1.m1.1.5.7.2a" xref="p1.1.m1.1.5.1.cmml">⁡</mo>
          <mrow id="p1.1.m1.1.5.7.2.1" xref="p1.1.m1.1.5.1.cmml">
            <mo id="p1.1.m1.1.5.4" xref="p1.1.m1.1.5.1.cmml">(</mo>
            <mrow id="p1.1.m1.1.5.5" xref="p1.1.m1.1.5.5.cmml">
              <mi id="p1.1.m1.1.5.5.1" xref="p1.1.m1.1.5.5.1.cmml">ζ</mi>
              <mo id="p1.1.m1.1.5.5.4" xref="p1.1.m1.1.5.5.4.cmml">⁢</mo>
              <msup id="p1.1.m1.1.5.5.5" xref="p1.1.m1.1.5.5.5.cmml">
                <mi id="p1.1.m1.1.5.5.2" xref="p1.1.m1.1.5.5.2.cmml">e</mi>
                <mrow id="p1.1.m1.1.5.5.3.1" xref="p1.1.m1.1.5.5.3.1.cmml">
                  <mo id="p1.1.m1.1.5.5.3.1.1" xref="p1.1.m1.1.5.5.3.1.1.cmml">-</mo>
                  <mrow id="p1.1.m1.1.5.5.3.1.6" xref="p1.1.m1.1.5.5.3.1.6.cmml">
                    <mrow id="p1.1.m1.1.5.5.3.1.6.1" xref="p1.1.m1.1.5.5.3.1.6.1.cmml">
                      <mi id="p1.1.m1.1.5.5.3.1.2" xref="p1.1.m1.1.5.5.3.1.2.cmml">π</mi>
                      <mo id="p1.1.m1.1.5.5.3.1.6.1.1" xref="p1.1.m1.1.5.5.3.1.6.1.1.cmml">⁢</mo>
                      <mi id="p1.1.m1.1.5.5.3.1.3" xref="p1.1.m1.1.5.5.3.1.3.cmml">i</mi>
                    </mrow>
                    <mo id="p1.1.m1.1.5.5.3.1.4" xref="p1.1.m1.1.5.5.3.1.4.cmml">/</mo>
                    <mn id="p1.1.m1.1.5.5.3.1.5" xref="p1.1.m1.1.5.5.3.1.5.cmml">2</mn>
                  </mrow>
                </mrow>
              </msup>
            </mrow>
            <mo id="p1.1.m1.1.5.6" xref="p1.1.m1.1.5.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
      <mrow id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">
        <mfrac id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
          <mn id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">1</mn>
          <mn id="p1.1.m1.1.7.3" xref="p1.1.m1.1.7.3.cmml">2</mn>
        </mfrac>
        <mo id="p1.1.m1.1.12.2.1" xref="p1.1.m1.1.12.2.1.cmml">⁢</mo>
        <msqrt id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
          <mrow id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">
            <mi id="p1.1.m1.1.8.2.1" xref="p1.1.m1.1.8.2.1.cmml">z</mi>
            <mo id="p1.1.m1.1.8.2.2" xref="p1.1.m1.1.8.2.2.cmml">/</mo>
            <mn id="p1.1.m1.1.8.2.3" xref="p1.1.m1.1.8.2.3.cmml">3</mn>
          </mrow>
        </msqrt>
        <mo id="p1.1.m1.1.12.2.1a" xref="p1.1.m1.1.12.2.1.cmml">⁢</mo>
        <msup id="p1.1.m1.1.12.2.2" xref="p1.1.m1.1.12.2.2.cmml">
          <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">e</mi>
          <mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
            <mo id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">-</mo>
            <mrow id="p1.1.m1.1.10.1.6" xref="p1.1.m1.1.10.1.6.cmml">
              <mrow id="p1.1.m1.1.10.1.6.1" xref="p1.1.m1.1.10.1.6.1.cmml">
                <mi id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">π</mi>
                <mo id="p1.1.m1.1.10.1.6.1.1" xref="p1.1.m1.1.10.1.6.1.1.cmml">⁢</mo>
                <mi id="p1.1.m1.1.10.1.3" xref="p1.1.m1.1.10.1.3.cmml">i</mi>
              </mrow>
              <mo id="p1.1.m1.1.10.1.4" xref="p1.1.m1.1.10.1.4.cmml">/</mo>
              <mn id="p1.1.m1.1.10.1.5" xref="p1.1.m1.1.10.1.5.cmml">3</mn>
            </mrow>
          </mrow>
        </msup>
        <mo id="p1.1.m1.1.12.2.1b" xref="p1.1.m1.1.12.2.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.11.7.2" xref="p1.1.m1.1.11.1.cmml">
          <msubsup id="p1.1.m1.1.11.2.1.5" xref="p1.1.m1.1.11.2.1.1.cmml">
            <mi id="p1.1.m1.1.11.2.1.2" xref="p1.1.m1.1.11.2.1.1.1.cmml">H</mi>
            <mrow id="p1.1.m1.1.11.2.1.4.1" xref="p1.1.m1.1.11.2.1.4.1.cmml">
              <mo id="p1.1.m1.1.11.2.1.4.1.1.1" xref="p1.1.m1.1.11.2.1.4.1.1.1.cmml">-</mo>
              <mrow id="p1.1.m1.1.11.2.1.4.1.1.5" xref="p1.1.m1.1.11.2.1.4.1.1.5.cmml">
                <mn id="p1.1.m1.1.11.2.1.4.1.1.2" xref="p1.1.m1.1.11.2.1.4.1.1.2.cmml">1</mn>
                <mo id="p1.1.m1.1.11.2.1.4.1.1.3" xref="p1.1.m1.1.11.2.1.4.1.1.3.cmml">/</mo>
                <mn id="p1.1.m1.1.11.2.1.4.1.1.4" xref="p1.1.m1.1.11.2.1.4.1.1.4.cmml">3</mn>
              </mrow>
            </mrow>
            <mrow id="p1.1.m1.1.11.2.1.3.1" xref="p1.1.m1.1.11.2.1.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.11.2.1.3.1.1" xref="p1.1.m1.1.11.2.1.1.1.cmml">(</mo>
              <mn id="p1.1.m1.1.11.2.1.3.1.2" xref="p1.1.m1.1.11.2.1.1.1.cmml">2</mn>
              <mo stretchy="false" id="p1.1.m1.1.11.2.1.3.1.3" xref="p1.1.m1.1.11.2.1.1.1.cmml">)</mo>
            </mrow>
          </msubsup>
          <mo id="p1.1.m1.1.11.7.2a" xref="p1.1.m1.1.11.1.cmml">⁡</mo>
          <mrow id="p1.1.m1.1.11.7.2.1" xref="p1.1.m1.1.11.1.cmml">
            <mo id="p1.1.m1.1.11.4" xref="p1.1.m1.1.11.1.cmml">(</mo>
            <mrow id="p1.1.m1.1.11.5" xref="p1.1.m1.1.11.5.cmml">
              <mi id="p1.1.m1.1.11.5.1" xref="p1.1.m1.1.11.5.1.cmml">ζ</mi>
              <mo id="p1.1.m1.1.11.5.4" xref="p1.1.m1.1.11.5.4.cmml">⁢</mo>
              <msup id="p1.1.m1.1.11.5.5" xref="p1.1.m1.1.11.5.5.cmml">
                <mi id="p1.1.m1.1.11.5.2" xref="p1.1.m1.1.11.5.2.cmml">e</mi>
                <mrow id="p1.1.m1.1.11.5.3.1" xref="p1.1.m1.1.11.5.3.1.cmml">
                  <mo id="p1.1.m1.1.11.5.3.1.1" xref="p1.1.m1.1.11.5.3.1.1.cmml">-</mo>
                  <mrow id="p1.1.m1.1.11.5.3.1.6" xref="p1.1.m1.1.11.5.3.1.6.cmml">
                    <mrow id="p1.1.m1.1.11.5.3.1.6.1" xref="p1.1.m1.1.11.5.3.1.6.1.cmml">
                      <mi id="p1.1.m1.1.11.5.3.1.2" xref="p1.1.m1.1.11.5.3.1.2.cmml">π</mi>
                      <mo id="p1.1.m1.1.11.5.3.1.6.1.1" xref="p1.1.m1.1.11.5.3.1.6.1.1.cmml">⁢</mo>
                      <mi id="p1.1.m1.1.11.5.3.1.3" xref="p1.1.m1.1.11.5.3.1.3.cmml">i</mi>
                    </mrow>
                    <mo id="p1.1.m1.1.11.5.3.1.4" xref="p1.1.m1.1.11.5.3.1.4.cmml">/</mo>
                    <mn id="p1.1.m1.1.11.5.3.1.5" xref="p1.1.m1.1.11.5.3.1.5.cmml">2</mn>
                  </mrow>
                </mrow>
              </msup>
            </mrow>
            <mo id="p1.1.m1.1.11.6" xref="p1.1.m1.1.11.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
        <eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
        <apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
          <times id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1.1"/>
          <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
            <divide id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1"/>
            <cn type="integer" id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">1</cn>
            <cn type="integer" id="p1.1.m1.1.1.3.cmml" xref="p1.1.m1.1.1.3">2</cn>
          </apply>
          <apply id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
            <root id="p1.1.m1.1.2a.cmml" xref="p1.1.m1.1.2"/>
            <apply id="p1.1.m1.1.2.2.cmml" xref="p1.1.m1.1.2.2">
              <divide id="p1.1.m1.1.2.2.2.cmml" xref="p1.1.m1.1.2.2.2"/>
              <ci id="p1.1.m1.1.2.2.1.cmml" xref="p1.1.m1.1.2.2.1">𝑧</ci>
              <cn type="integer" id="p1.1.m1.1.2.2.3.cmml" xref="p1.1.m1.1.2.2.3">3</cn>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.12.1.2.cmml" xref="p1.1.m1.1.12.1.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.12.1.2.1.cmml" xref="p1.1.m1.1.12.1.2">superscript</csymbol>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑒</ci>
            <apply id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">
              <minus id="p1.1.m1.1.4.1.1.cmml" xref="p1.1.m1.1.4.1.1"/>
              <apply id="p1.1.m1.1.4.1.7.cmml" xref="p1.1.m1.1.4.1.7">
                <divide id="p1.1.m1.1.4.1.5.cmml" xref="p1.1.m1.1.4.1.5"/>
                <apply id="p1.1.m1.1.4.1.7.1.cmml" xref="p1.1.m1.1.4.1.7.1">
                  <times id="p1.1.m1.1.4.1.7.1.1.cmml" xref="p1.1.m1.1.4.1.7.1.1"/>
                  <cn type="integer" id="p1.1.m1.1.4.1.2.cmml" xref="p1.1.m1.1.4.1.2">2</cn>
                  <ci id="p1.1.m1.1.4.1.3.cmml" xref="p1.1.m1.1.4.1.3">𝜋</ci>
                  <ci id="p1.1.m1.1.4.1.4.cmml" xref="p1.1.m1.1.4.1.4">𝑖</ci>
                </apply>
                <cn type="integer" id="p1.1.m1.1.4.1.6.cmml" xref="p1.1.m1.1.4.1.6">3</cn>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.7.2">
            <apply id="p1.1.m1.1.5.2.1.1.cmml" xref="p1.1.m1.1.5.2.1.5">
              <csymbol cd="dlmf" id="p1.1.m1.1.5.2.1.1.1.cmml" xref="p1.1.m1.1.5.2.1.2">Hankel-H-2-Bessel-third-kind</csymbol>
              <apply id="p1.1.m1.1.5.2.1.4.1.cmml" xref="p1.1.m1.1.5.2.1.4.1">
                <divide id="p1.1.m1.1.5.2.1.4.1.1.2.cmml" xref="p1.1.m1.1.5.2.1.4.1.1.2"/>
                <cn type="integer" id="p1.1.m1.1.5.2.1.4.1.1.1.cmml" xref="p1.1.m1.1.5.2.1.4.1.1.1">1</cn>
                <cn type="integer" id="p1.1.m1.1.5.2.1.4.1.1.3.cmml" xref="p1.1.m1.1.5.2.1.4.1.1.3">3</cn>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.5.5.cmml" xref="p1.1.m1.1.5.5">
              <times id="p1.1.m1.1.5.5.4.cmml" xref="p1.1.m1.1.5.5.4"/>
              <ci id="p1.1.m1.1.5.5.1.cmml" xref="p1.1.m1.1.5.5.1">𝜁</ci>
              <apply id="p1.1.m1.1.5.5.5.cmml" xref="p1.1.m1.1.5.5.5">
                <csymbol cd="ambiguous" id="p1.1.m1.1.5.5.5.1.cmml" xref="p1.1.m1.1.5.5.5">superscript</csymbol>
                <ci id="p1.1.m1.1.5.5.2.cmml" xref="p1.1.m1.1.5.5.2">𝑒</ci>
                <apply id="p1.1.m1.1.5.5.3.1.cmml" xref="p1.1.m1.1.5.5.3.1">
                  <minus id="p1.1.m1.1.5.5.3.1.1.cmml" xref="p1.1.m1.1.5.5.3.1.1"/>
                  <apply id="p1.1.m1.1.5.5.3.1.6.cmml" xref="p1.1.m1.1.5.5.3.1.6">
                    <divide id="p1.1.m1.1.5.5.3.1.4.cmml" xref="p1.1.m1.1.5.5.3.1.4"/>
                    <apply id="p1.1.m1.1.5.5.3.1.6.1.cmml" xref="p1.1.m1.1.5.5.3.1.6.1">
                      <times id="p1.1.m1.1.5.5.3.1.6.1.1.cmml" xref="p1.1.m1.1.5.5.3.1.6.1.1"/>
                      <ci id="p1.1.m1.1.5.5.3.1.2.cmml" xref="p1.1.m1.1.5.5.3.1.2">𝜋</ci>
                      <ci id="p1.1.m1.1.5.5.3.1.3.cmml" xref="p1.1.m1.1.5.5.3.1.3">𝑖</ci>
                    </apply>
                    <cn type="integer" id="p1.1.m1.1.5.5.3.1.5.cmml" xref="p1.1.m1.1.5.5.3.1.5">2</cn>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2">
          <times id="p1.1.m1.1.12.2.1.cmml" xref="p1.1.m1.1.12.2.1"/>
          <apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
            <divide id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7"/>
            <cn type="integer" id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">1</cn>
            <cn type="integer" id="p1.1.m1.1.7.3.cmml" xref="p1.1.m1.1.7.3">2</cn>
          </apply>
          <apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
            <root id="p1.1.m1.1.8a.cmml" xref="p1.1.m1.1.8"/>
            <apply id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">
              <divide id="p1.1.m1.1.8.2.2.cmml" xref="p1.1.m1.1.8.2.2"/>
              <ci id="p1.1.m1.1.8.2.1.cmml" xref="p1.1.m1.1.8.2.1">𝑧</ci>
              <cn type="integer" id="p1.1.m1.1.8.2.3.cmml" xref="p1.1.m1.1.8.2.3">3</cn>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.12.2.2.cmml" xref="p1.1.m1.1.12.2.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.12.2.2.1.cmml" xref="p1.1.m1.1.12.2.2">superscript</csymbol>
            <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑒</ci>
            <apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
              <minus id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1"/>
              <apply id="p1.1.m1.1.10.1.6.cmml" xref="p1.1.m1.1.10.1.6">
                <divide id="p1.1.m1.1.10.1.4.cmml" xref="p1.1.m1.1.10.1.4"/>
                <apply id="p1.1.m1.1.10.1.6.1.cmml" xref="p1.1.m1.1.10.1.6.1">
                  <times id="p1.1.m1.1.10.1.6.1.1.cmml" xref="p1.1.m1.1.10.1.6.1.1"/>
                  <ci id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2">𝜋</ci>
                  <ci id="p1.1.m1.1.10.1.3.cmml" xref="p1.1.m1.1.10.1.3">𝑖</ci>
                </apply>
                <cn type="integer" id="p1.1.m1.1.10.1.5.cmml" xref="p1.1.m1.1.10.1.5">3</cn>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.7.2">
            <apply id="p1.1.m1.1.11.2.1.1.cmml" xref="p1.1.m1.1.11.2.1.5">
              <csymbol cd="dlmf" id="p1.1.m1.1.11.2.1.1.1.cmml" xref="p1.1.m1.1.11.2.1.2">Hankel-H-2-Bessel-third-kind</csymbol>
              <apply id="p1.1.m1.1.11.2.1.4.1.cmml" xref="p1.1.m1.1.11.2.1.4.1">
                <minus id="p1.1.m1.1.11.2.1.4.1.1.1.cmml" xref="p1.1.m1.1.11.2.1.4.1.1.1"/>
                <apply id="p1.1.m1.1.11.2.1.4.1.1.5.cmml" xref="p1.1.m1.1.11.2.1.4.1.1.5">
                  <divide id="p1.1.m1.1.11.2.1.4.1.1.3.cmml" xref="p1.1.m1.1.11.2.1.4.1.1.3"/>
                  <cn type="integer" id="p1.1.m1.1.11.2.1.4.1.1.2.cmml" xref="p1.1.m1.1.11.2.1.4.1.1.2">1</cn>
                  <cn type="integer" id="p1.1.m1.1.11.2.1.4.1.1.4.cmml" xref="p1.1.m1.1.11.2.1.4.1.1.4">3</cn>
                </apply>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.11.5.cmml" xref="p1.1.m1.1.11.5">
              <times id="p1.1.m1.1.11.5.4.cmml" xref="p1.1.m1.1.11.5.4"/>
              <ci id="p1.1.m1.1.11.5.1.cmml" xref="p1.1.m1.1.11.5.1">𝜁</ci>
              <apply id="p1.1.m1.1.11.5.5.cmml" xref="p1.1.m1.1.11.5.5">
                <csymbol cd="ambiguous" id="p1.1.m1.1.11.5.5.1.cmml" xref="p1.1.m1.1.11.5.5">superscript</csymbol>
                <ci id="p1.1.m1.1.11.5.2.cmml" xref="p1.1.m1.1.11.5.2">𝑒</ci>
                <apply id="p1.1.m1.1.11.5.3.1.cmml" xref="p1.1.m1.1.11.5.3.1">
                  <minus id="p1.1.m1.1.11.5.3.1.1.cmml" xref="p1.1.m1.1.11.5.3.1.1"/>
                  <apply id="p1.1.m1.1.11.5.3.1.6.cmml" xref="p1.1.m1.1.11.5.3.1.6">
                    <divide id="p1.1.m1.1.11.5.3.1.4.cmml" xref="p1.1.m1.1.11.5.3.1.4"/>
                    <apply id="p1.1.m1.1.11.5.3.1.6.1.cmml" xref="p1.1.m1.1.11.5.3.1.6.1">
                      <times id="p1.1.m1.1.11.5.3.1.6.1.1.cmml" xref="p1.1.m1.1.11.5.3.1.6.1.1"/>
                      <ci id="p1.1.m1.1.11.5.3.1.2.cmml" xref="p1.1.m1.1.11.5.3.1.2">𝜋</ci>
                      <ci id="p1.1.m1.1.11.5.3.1.3.cmml" xref="p1.1.m1.1.11.5.3.1.3">𝑖</ci>
                    </apply>
                    <cn type="integer" id="p1.1.m1.1.11.5.3.1.5.cmml" xref="p1.1.m1.1.11.5.3.1.5">2</cn>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}{H^{(2)}_{1/3}}%
\left(\zeta e^{-\pi i/2}\right)=\tfrac{1}{2}\sqrt{z/3}e^{-\pi i/3}{H^{(2)}_{-1%
/3}}\left(\zeta e^{-\pi i/2}\right)}}</annotation>
  </semantics>
</math>

SVG (19.91 KB / 5.043 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	0.0002	354792	{main}( )	.../index.php:0
2	0.0214	1736000	wfIndexMain( )	.../index.php:46
3	0.0214	1736096	MediaWiki->run( )	.../index.php:50
4	0.0214	1736096	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0218	1749464	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0614	2009440	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 = 1686043199.9498; 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.63458.32 on revision:63458\n</p><p>* Page found: <a href="/wiki/Results_of_Airy_and_Related_Functions#math.63458.32" title="Results of Airy and Related Functions">Results of Airy and Related Functions</a> (eq math.63458.32) </p><a href="/index.php?title=Results_of_Airy_and_Related_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a href="/w'...; 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 = '20230606092000'; 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	0.0615	2013344	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0616	2013344	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0616	2013344	FormulaInfo->DisplayInfo( $oldID = '63458', $eid = 'math.63458.32' )	.../FormulaInfo.php:45
10	0.9705	5238440	FormulaInfo::DisplayTranslations( $tex = '\\tfrac{1}{2}\\sqrt{z/3}e^{-2\\pi i/3}\\HankelH{2}{1/3}@{\\zeta e^{-\\pi i/2}} = \\tfrac{1}{2}\\sqrt{z/3}e^{-\\pi i/3}\\HankelH{2}{-1/3}@{\\zeta e^{-\\pi i/2}}' )	.../FormulaInfo.php:168
11	0.9903	5286192	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	0.0002	354792	{main}( )	.../index.php:0
2	0.0214	1736000	wfIndexMain( )	.../index.php:46
3	0.0214	1736096	MediaWiki->run( )	.../index.php:50
4	0.0214	1736096	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0218	1749464	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0614	2009440	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 = 1686043199.9498; 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.63458.32 on revision:63458\n</p><p>* Page found: <a href="/wiki/Results_of_Airy_and_Related_Functions#math.63458.32" title="Results of Airy and Related Functions">Results of Airy and Related Functions</a> (eq math.63458.32) </p><a href="/index.php?title=Results_of_Airy_and_Related_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a href="/w'...; 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 = '20230606092000'; 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	0.0615	2013344	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0616	2013344	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0616	2013344	FormulaInfo->DisplayInfo( $oldID = '63458', $eid = 'math.63458.32' )	.../FormulaInfo.php:45
10	0.9705	5238440	FormulaInfo::DisplayTranslations( $tex = '\\tfrac{1}{2}\\sqrt{z/3}e^{-2\\pi i/3}\\HankelH{2}{1/3}@{\\zeta e^{-\\pi i/2}} = \\tfrac{1}{2}\\sqrt{z/3}e^{-\\pi i/3}\\HankelH{2}{-1/3}@{\\zeta e^{-\\pi i/2}}' )	.../FormulaInfo.php:168
11	0.9903	5286192	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	0.0002	354792	{main}( )	.../index.php:0
2	0.0214	1736000	wfIndexMain( )	.../index.php:46
3	0.0214	1736096	MediaWiki->run( )	.../index.php:50
4	0.0214	1736096	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0218	1749464	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0614	2009440	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 = 1686043199.9498; 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.63458.32 on revision:63458\n</p><p>* Page found: <a href="/wiki/Results_of_Airy_and_Related_Functions#math.63458.32" title="Results of Airy and Related Functions">Results of Airy and Related Functions</a> (eq math.63458.32) </p><a href="/index.php?title=Results_of_Airy_and_Related_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a href="/w'...; 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 = '20230606092000'; 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	0.0615	2013344	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0616	2013344	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0616	2013344	FormulaInfo->DisplayInfo( $oldID = '63458', $eid = 'math.63458.32' )	.../FormulaInfo.php:45
10	0.9705	5238440	FormulaInfo::DisplayTranslations( $tex = '\\tfrac{1}{2}\\sqrt{z/3}e^{-2\\pi i/3}\\HankelH{2}{1/3}@{\\zeta e^{-\\pi i/2}} = \\tfrac{1}{2}\\sqrt{z/3}e^{-\\pi i/3}\\HankelH{2}{-1/3}@{\\zeta e^{-\\pi i/2}}' )	.../FormulaInfo.php:168
11	0.9903	5286192	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	1.0000	5305552	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	0.0002	354792	{main}( )	.../index.php:0
2	0.0214	1736000	wfIndexMain( )	.../index.php:46
3	0.0214	1736096	MediaWiki->run( )	.../index.php:50
4	0.0214	1736096	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0218	1749464	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0614	2009440	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 = 1686043199.9498; 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.63458.32 on revision:63458\n</p><p>* Page found: <a href="/wiki/Results_of_Airy_and_Related_Functions#math.63458.32" title="Results of Airy and Related Functions">Results of Airy and Related Functions</a> (eq math.63458.32) </p><a href="/index.php?title=Results_of_Airy_and_Related_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a href="/w'...; 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 = '20230606092000'; 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	0.0615	2013344	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0616	2013344	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0616	2013344	FormulaInfo->DisplayInfo( $oldID = '63458', $eid = 'math.63458.32' )	.../FormulaInfo.php:45
10	0.9705	5238440	FormulaInfo::DisplayTranslations( $tex = '\\tfrac{1}{2}\\sqrt{z/3}e^{-2\\pi i/3}\\HankelH{2}{1/3}@{\\zeta e^{-\\pi i/2}} = \\tfrac{1}{2}\\sqrt{z/3}e^{-\\pi i/3}\\HankelH{2}{-1/3}@{\\zeta e^{-\\pi i/2}}' )	.../FormulaInfo.php:168
11	1.0018	5322896	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	0.0002	354792	{main}( )	.../index.php:0
2	0.0214	1736000	wfIndexMain( )	.../index.php:46
3	0.0214	1736096	MediaWiki->run( )	.../index.php:50
4	0.0214	1736096	MediaWiki->main( )	.../MediaWiki.php:573
5	0.0218	1749464	MediaWiki->performRequest( )	.../MediaWiki.php:917
6	0.0614	2009440	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 = 1686043199.9498; 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.63458.32 on revision:63458\n</p><p>* Page found: <a href="/wiki/Results_of_Airy_and_Related_Functions#math.63458.32" title="Results of Airy and Related Functions">Results of Airy and Related Functions</a> (eq math.63458.32) </p><a href="/index.php?title=Results_of_Airy_and_Related_Functions&action=purge&mathpurge=true">(force rerendering)</a><p>Occurrences on the following pages:\n</p><ul><li><a href="/w'...; 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 = '20230606092000'; 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	0.0615	2013344	SpecialPage->run( $subPage = NULL )	.../SpecialPageFactory.php:1460
8	0.0616	2013344	FormulaInfo->execute( $par = NULL )	.../SpecialPage.php:700
9	0.0616	2013344	FormulaInfo->DisplayInfo( $oldID = '63458', $eid = 'math.63458.32' )	.../FormulaInfo.php:45
10	0.9705	5238440	FormulaInfo::DisplayTranslations( $tex = '\\tfrac{1}{2}\\sqrt{z/3}e^{-2\\pi i/3}\\HankelH{2}{1/3}@{\\zeta e^{-\\pi i/2}} = \\tfrac{1}{2}\\sqrt{z/3}e^{-\\pi i/3}\\HankelH{2}{-1/3}@{\\zeta e^{-\\pi i/2}}' )	.../FormulaInfo.php:168
11	1.0018	5322896	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