data/mathoid/248.mml
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xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="upper S Subscript normal p normal r normal o normal b normal e Baseline equals minus left-parenthesis upper T 4 upper L right-parenthesis integral d Superscript 4 Baseline x StartRoot negative g EndRoot left-bracket one-half left-parenthesis 1 plus StartFraction g Subscript s Baseline pi sine theta Over 2 left-parenthesis upper M Subscript s Baseline upper L right-parenthesis left-parenthesis upper M Subscript s Baseline y right-parenthesis squared EndFraction right-parenthesis StartAbsoluteValue partial-differential y EndAbsoluteValue squared minus 2 left-parenthesis 1 minus StartFraction g Subscript s Baseline pi tangent cubed theta Over 8 left-parenthesis upper M Subscript s Baseline upper L right-parenthesis left-parenthesis upper M Subscript s Baseline y right-parenthesis squared EndFraction right-parenthesis right-bracket">
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<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="29" data-semantic-parent="139" data-semantic-operator="fenced">[</mo>
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<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="33" data-semantic-parent="75" data-semantic-operator="fenced">(</mo>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="37" data-semantic-parent="38">s</mi>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="39" data-semantic-parent="47">π
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<mi data-semantic-type="function" data-semantic-role="prefix function" data-semantic-font="normal" data-semantic-id="40" data-semantic-parent="44" data-semantic-operator="appl">sin</mi>
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="48" data-semantic-parent="71">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="69" data-semantic-parent="71" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="70" data-semantic-parent="71" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="56" data-semantic-parent="58">M</mi>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="66" data-semantic-parent="67" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="61" data-semantic-parent="62">2</mn>
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<mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="74" data-semantic-parent="75" data-semantic-operator="fenced">)</mo>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="133" data-semantic-parent="134" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<msup data-semantic-type="superscript" data-semantic-role="neutral" data-semantic-id="81" data-semantic-children="131,80" data-semantic-parent="134" data-semantic-fencepointer="79">
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="85" data-semantic-parent="126">1</mn>
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<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="125" data-semantic-children="100,124" data-semantic-parent="126">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="100" data-semantic-children="89,90,97" data-semantic-content="98,99" data-semantic-parent="125">
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<mrow data-semantic-type="appl" data-semantic-role="prefix function" data-semantic-id="97" data-semantic-children="93,95" data-semantic-content="96,91" data-semantic-parent="100">
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="92" data-semantic-parent="93">3</mn>
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</mrow>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="124" data-semantic-children="101,118,115" data-semantic-content="122,123" data-semantic-parent="125">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="101" data-semantic-parent="124">8</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="122" data-semantic-parent="124" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="105" data-semantic-children="103,104" data-semantic-parent="117">
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="114" data-semantic-parent="115">2</mn>
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</mfrac>
</mrow>
</mrow>
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<annotation encoding="application/x-tex">S_{\rm {probe}}=-(T_{4}L)\int d^{4}x\,{\sqrt {-g}}\left[{1 \over 2}\left(1+{\frac {g_{s}\pi \sin \theta }{2(M_{s}L)(M_{s}y)^{2}}}\right)|\partial y|^{2}-2\left(1-{\frac {g_{s}\pi \tan ^{3}\theta }{8(M_{s}L)(M_{s}y)^{2}}}\right)\right]</annotation>
</semantics>
</math>