mathmlben
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Visualization for goldstandard
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text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="upper L n normal upper Gamma left-parenthesis z right-parenthesis equals left-parenthesis z minus one-half right-parenthesis ln z minus z plus one-half ln left-parenthesis 2 pi right-parenthesis plus 2 integral Subscript 0 Superscript normal infinity Baseline StartFraction arc tangent left-parenthesis t slash z right-parenthesis Over e Superscript 2 pi t Baseline minus 1 EndFraction normal d t">
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<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-id="0" data-semantic-parent="76" data-semantic-operator="appl">Ln</mi>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-id="2" data-semantic-parent="74" data-semantic-operator="appl">Γ
<!-- Γ -->
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<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="10" data-semantic-parent="14" data-semantic-operator="infixop,−">−
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="19" data-semantic-parent="72">z</mi>
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<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="20" data-semantic-parent="79" data-semantic-operator="infixop,−">−
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="21" data-semantic-parent="79">z</mi>
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<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="22" data-semantic-parent="82" 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="29" data-semantic-parent="32">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="31" data-semantic-parent="32" 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="30" data-semantic-parent="32">π
<!-- π -->
</mi>
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<mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="33" data-semantic-parent="34" data-semantic-operator="fenced">)</mo>
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<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="35" data-semantic-parent="82" 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="36" data-semantic-parent="84">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="83" data-semantic-parent="84" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<msubsup data-semantic-type="limboth" data-semantic-role="integral" data-semantic-id="40" data-semantic-children="37,38,39" data-semantic-parent="68">
<mo data-semantic-type="largeop" data-semantic-role="integral" data-semantic-id="37" data-semantic-parent="40" data-semantic-operator="integral">∫
<!-- ∫ -->
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="38" data-semantic-parent="40">0</mn>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="39" data-semantic-parent="40">∞
<!-- ∞ -->
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<mi data-semantic-type="function" data-semantic-role="prefix function" data-semantic-font="normal" data-semantic-id="41" data-semantic-parent="51" data-semantic-operator="appl">arctan</mi>
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<mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="45" data-semantic-parent="47" 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="46" data-semantic-parent="47">z</mi>
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<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="59" data-semantic-children="52,58" data-semantic-parent="62">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="52" data-semantic-parent="59">e</mi>
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="53" data-semantic-parent="58">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="56" data-semantic-parent="58" 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="54" data-semantic-parent="58">π
<!-- π -->
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="64" data-semantic-parent="67">d</mi>
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<annotation encoding="application/x-tex">\operatorname {Ln} \Gamma \left(z\right)=\left(z-{\tfrac {1}{2}}\right)\ln z-z+{\tfrac {1}{2}}\ln \left(2\pi \right)+2\int _{0}^{\infty }{\frac {\operatorname {arctan} \left(t/z\right)}{e^{2\pi t}-1}}\mathrm {d} t</annotation>
</semantics>
</math>