mathmlben
Version:
Visualization for goldstandard
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text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="StartFraction 1 Over 2 pi normal i EndFraction integral Subscript negative normal infinity Superscript left-parenthesis 0 plus right-parenthesis Baseline e Superscript z t plus one-half t Super Superscript negative 1 Baseline t Superscript kappa Baseline upper W Subscript kappa comma mu Baseline left-parenthesis t Superscript negative 1 Baseline right-parenthesis normal d t equals StartFraction 2 z Superscript negative kappa minus one-half Baseline Over normal upper Gamma left-parenthesis one-half plus mu minus kappa right-parenthesis normal upper Gamma left-parenthesis one-half minus mu minus kappa right-parenthesis EndFraction upper K Subscript 2 mu Baseline left-parenthesis 2 StartRoot z EndRoot right-parenthesis">
<semantics>
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<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="7" data-semantic-children="0,6" data-semantic-parent="125">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="0" data-semantic-parent="7">1</mn>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="6" data-semantic-children="1,2,3" data-semantic-content="4,5" data-semantic-parent="7">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="1" data-semantic-parent="6">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="4" data-semantic-parent="6" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="6">π
<!-- π -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="5" data-semantic-parent="6" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="3" data-semantic-parent="6">i</mi>
</mrow>
</mrow>
</mfrac>
</mrow>
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<mrow data-semantic-type="integral" data-semantic-role="integral" data-semantic-id="123" data-semantic-children="18,122,119" data-semantic-content="8" data-semantic-parent="125">
<msubsup data-semantic-type="limboth" data-semantic-role="integral" data-semantic-id="18" data-semantic-children="8,11,17" data-semantic-parent="123">
<mo data-semantic-type="largeop" data-semantic-role="integral" data-semantic-id="8" data-semantic-parent="18" data-semantic-operator="integral">∫
<!-- ∫ -->
</mo>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="10" data-semantic-parent="11">∞
<!-- ∞ -->
</mi>
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<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="113" data-semantic-children="111" data-semantic-content="106,112" data-semantic-parent="115">
<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="106" data-semantic-parent="113" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="111" data-semantic-children="107,109" data-semantic-content="110" data-semantic-parent="113">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="107" data-semantic-parent="111">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="110" data-semantic-parent="111" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt data-semantic-type="sqrt" data-semantic-role="unknown" data-semantic-id="109" data-semantic-children="108" data-semantic-parent="111">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="108" data-semantic-parent="109">z</mi>
</msqrt>
</mrow>
</mrow>
<mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="112" data-semantic-parent="113" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<annotation encoding="application/x-tex">{\frac {1}{2\pi \mathrm {i} }}\int _{-\infty }^{(0+)}e^{zt+{\frac {1}{2}}t^{-1}}t^{\kappa }W_{\kappa ,\mu }\left(t^{-1}\right)\mathrm {d} t={\frac {2z^{-\kappa -{\frac {1}{2}}}}{\Gamma \left({\frac {1}{2}}+\mu -\kappa \right)\Gamma \left({\frac {1}{2}}-\mu -\kappa \right)}}K_{2\mu }\left(2{\sqrt {z}}\right)</annotation>
</semantics>
</math>