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="integral Subscript 0 Superscript normal infinity Baseline StartFraction t Superscript nu plus 1 Baseline upper J Subscript nu Baseline left-parenthesis a t right-parenthesis Over left-parenthesis t squared plus b squared right-parenthesis Superscript mu plus 1 Baseline EndFraction normal d t equals StartFraction a Superscript mu Baseline b Superscript nu minus mu Baseline Over 2 Superscript mu Baseline normal upper Gamma left-parenthesis mu plus 1 right-parenthesis EndFraction upper K Subscript nu minus mu Baseline left-parenthesis a b right-parenthesis">
<semantics>
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<mo data-semantic-type="largeop" data-semantic-role="integral" data-semantic-id="0" data-semantic-parent="3" data-semantic-operator="integral">∫
<!-- ∫ -->
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="1" data-semantic-parent="3">0</mn>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="2" data-semantic-parent="3">∞
<!-- ∞ -->
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="4" data-semantic-parent="9">t</mi>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="5" data-semantic-parent="8">ν
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<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="10" data-semantic-parent="12" data-semantic-operator="appl">J</mi>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="11" data-semantic-parent="12">ν
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<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="13" data-semantic-parent="19" data-semantic-operator="fenced">(</mo>
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<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="39" data-semantic-children="38" data-semantic-content="24,32" data-semantic-parent="37">
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="25" data-semantic-parent="27">t</mi>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="29" data-semantic-parent="31">b</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="32" data-semantic-parent="39">)</mo>
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<mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="36" data-semantic-children="33,35" data-semantic-content="34" data-semantic-parent="37">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="33" data-semantic-parent="36">μ
<!-- μ -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="34" data-semantic-parent="36" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="35" data-semantic-parent="36">1</mn>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="41" data-semantic-parent="86">d</mi>
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<mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="85" data-semantic-parent="86" data-semantic-added="true" data-semantic-operator="punctuated"></mo>
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<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="43" data-semantic-parent="90" data-semantic-operator="relseq,=">=</mo>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="44" data-semantic-parent="46">a</mi>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="45" data-semantic-parent="46">μ
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="47" data-semantic-parent="52">b</mi>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="48" data-semantic-parent="51">ν
<!-- ν -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="49" data-semantic-parent="51" data-semantic-operator="infixop,−">−
<!-- − -->
</mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="50" data-semantic-parent="51">μ
<!-- μ -->
</mi>
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<msup data-semantic-type="superscript" data-semantic-role="integer" data-semantic-id="57" data-semantic-children="55,56" data-semantic-parent="68">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="55" data-semantic-parent="57">2</mn>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="56" data-semantic-parent="57">μ
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-id="58" data-semantic-parent="68">Γ
<!-- Γ -->
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="60" data-semantic-parent="63">μ
<!-- μ -->
</mi>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="73" data-semantic-parent="74">μ
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<annotation encoding="application/x-tex">\int _{0}^{\infty }{\frac {t^{\nu +1}J_{\nu }\left(at\right)}{(t^{2}+b^{2})^{\mu +1}}}\mathrm {d} t={\frac {a^{\mu }b^{\nu -\mu }}{2^{\mu }\Gamma \left(\mu +1\right)}}K_{\nu -\mu }\left(ab\right)</annotation>
</semantics>
</math>