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 J prime Subscript nu Baseline left-parenthesis j Subscript nu comma m Baseline right-parenthesis tilde left-parenthesis negative 1 right-parenthesis Superscript m Baseline StartFraction left-parenthesis 2 slash nu right-parenthesis Superscript two-thirds Baseline Over pi upper M left-parenthesis a Subscript m Baseline right-parenthesis EndFraction sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts StartFraction beta Subscript k Baseline Over nu Superscript 2 k slash 3 Baseline EndFraction">
<semantics>
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<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="4" 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="1" data-semantic-parent="4">ν
<!-- ν -->
</mi>
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<mo data-semantic-type="punctuation" data-semantic-role="prime" data-semantic-id="2" data-semantic-parent="4">′</mo>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="6" data-semantic-parent="11">j</mi>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="7" data-semantic-parent="10">ν
<!-- ν -->
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<mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="8" data-semantic-parent="10" data-semantic-operator="punctuated">,</mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="9" data-semantic-parent="10">m</mi>
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<mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="12" data-semantic-parent="13" data-semantic-operator="fenced">)</mo>
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<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="14" data-semantic-parent="73" data-semantic-operator="relseq,∼">∼
<!-- ∼ -->
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="15" data-semantic-parent="66">(</mo>
<mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="65" data-semantic-children="17" data-semantic-content="16" data-semantic-parent="66">
<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="16" data-semantic-parent="65" data-semantic-operator="prefixop,−">−
<!-- − -->
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="17" data-semantic-parent="65">1</mn>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="18" data-semantic-parent="66">)</mo>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="19" data-semantic-parent="20">m</mi>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="70" data-semantic-parent="72" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="44" data-semantic-children="29,43" data-semantic-parent="72">
<mrow>
<msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="29" data-semantic-children="31,28" data-semantic-parent="44" data-semantic-fencepointer="25">
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="31" data-semantic-children="30" data-semantic-content="21,25" data-semantic-parent="29">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="21" data-semantic-parent="31">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="30" data-semantic-children="22,24" data-semantic-content="23" data-semantic-parent="31">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="22" data-semantic-parent="30">2</mn>
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<mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="23" data-semantic-parent="30" data-semantic-operator="infixop,/">/</mo>
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="24" data-semantic-parent="30">ν
<!-- ν -->
</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="25" data-semantic-parent="31">)</mo>
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<mfrac data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-id="28" data-semantic-children="26,27" data-semantic-parent="29">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="26" data-semantic-parent="28">2</mn>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="27" data-semantic-parent="28">3</mn>
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<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="43" data-semantic-children="32,41" data-semantic-content="42" data-semantic-parent="44">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="32" data-semantic-parent="43">π
<!-- π -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="42" data-semantic-parent="43" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="33" data-semantic-parent="41" data-semantic-operator="appl">M</mi>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="40" data-semantic-parent="41" data-semantic-added="true" data-semantic-operator="appl"></mo>
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<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="34" data-semantic-parent="39" data-semantic-operator="fenced">(</mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="37" data-semantic-children="35,36" data-semantic-parent="39">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="35" data-semantic-parent="37">a</mi>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="36" data-semantic-parent="37">m</mi>
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<mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="38" data-semantic-parent="39" data-semantic-operator="fenced">)</mo>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="71" data-semantic-parent="72" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="bigop" data-semantic-role="sum" data-semantic-id="67" data-semantic-children="51,64" data-semantic-content="45" data-semantic-parent="72">
<munderover data-semantic-type="limboth" data-semantic-role="sum" data-semantic-id="51" data-semantic-children="45,49,50" data-semantic-parent="67">
<mo data-semantic-type="largeop" data-semantic-role="sum" data-semantic-id="45" data-semantic-parent="51" data-semantic-operator="bigop">∑
<!-- ∑ -->
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="46" data-semantic-parent="49">k</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="49">0</mn>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="50" data-semantic-parent="51">∞
<!-- ∞ -->
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<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="64" data-semantic-children="54,63" data-semantic-parent="67">
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="52" data-semantic-parent="54">β
<!-- β -->
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="53" data-semantic-parent="54">k</mi>
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<!-- ν -->
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="56" data-semantic-parent="61">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="60" data-semantic-parent="61" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="57" data-semantic-parent="61">k</mi>
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<mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="58" data-semantic-parent="62" 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="59" data-semantic-parent="62">3</mn>
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<annotation encoding="application/x-tex">J_{\nu }'\left(j_{\nu ,m}\right)\sim (-1)^{m}{\frac {(2/\nu )^{\frac {2}{3}}}{\pi M\left(a_{m}\right)}}\sum _{k=0}^{\infty }{\frac {\beta _{k}}{\nu ^{2k/3}}}</annotation>
</semantics>
</math>