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mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="psi left-parenthesis StartFraction z plus 1 Over 2 EndFraction right-parenthesis minus psi left-parenthesis StartFraction z Over 2 EndFraction right-parenthesis equals 2 sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts StartFraction left-parenthesis negative 1 right-parenthesis Superscript k Baseline Over k plus z EndFraction"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="48" data-semantic-children="45,47" data-semantic-content="18"> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="45" data-semantic-children="44,42" data-semantic-content="10" data-semantic-parent="48"> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="44" data-semantic-children="0,9" data-semantic-content="43,0" data-semantic-parent="45"> <mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="44" data-semantic-operator="appl">ψ <!-- ψ --> </mi> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="43" data-semantic-parent="44" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="9" data-semantic-children="7" data-semantic-content="1,8" data-semantic-parent="44"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="1" data-semantic-parent="9" data-semantic-operator="fenced">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="7" data-semantic-children="5,6" data-semantic-parent="9"> <mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="5" data-semantic-children="2,4" data-semantic-content="3" data-semantic-parent="7"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="5">z</mi> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="3" data-semantic-parent="5" data-semantic-operator="infixop,+">+</mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="4" data-semantic-parent="5">1</mn> </mrow> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="6" data-semantic-parent="7">2</mn> </mfrac> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="8" data-semantic-parent="9" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="10" data-semantic-parent="45" data-semantic-operator="infixop,−"><!-- − --> </mo> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="42" data-semantic-children="11,17" data-semantic-content="41,11" data-semantic-parent="45"> <mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="11" data-semantic-parent="42" data-semantic-operator="appl">ψ <!-- ψ --> </mi> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="41" data-semantic-parent="42" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="17" data-semantic-children="15" data-semantic-content="12,16" data-semantic-parent="42"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="12" data-semantic-parent="17" data-semantic-operator="fenced">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="15" data-semantic-children="13,14" data-semantic-parent="17"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="13" data-semantic-parent="15">z</mi> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="14" data-semantic-parent="15">2</mn> </mfrac> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="16" data-semantic-parent="17" data-semantic-operator="fenced">)</mo> </mrow> </mrow> </mrow> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="18" data-semantic-parent="48" data-semantic-operator="relseq,=">=</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="47" data-semantic-children="19,40" data-semantic-content="46" data-semantic-parent="48"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="19" data-semantic-parent="47">2</mn> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="46" data-semantic-parent="47" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="bigop" data-semantic-role="sum" data-semantic-id="40" data-semantic-children="26,39" data-semantic-content="20" data-semantic-parent="47"> <munderover data-semantic-type="limboth" data-semantic-role="sum" data-semantic-id="26" data-semantic-children="20,24,25" data-semantic-parent="40"> <mo data-semantic-type="largeop" data-semantic-role="sum" data-semantic-id="20" data-semantic-parent="26" data-semantic-operator="bigop"><!-- ∑ --> </mo> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="24" data-semantic-children="21,23" data-semantic-content="22" data-semantic-parent="26"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="21" data-semantic-parent="24">k</mi> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="22" data-semantic-parent="24" data-semantic-operator="relseq,=">=</mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="23" data-semantic-parent="24">0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="25" data-semantic-parent="26"><!-- ∞ --> </mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="39" data-semantic-children="32,38" data-semantic-parent="40"> <mrow> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="32" data-semantic-children="34,31" data-semantic-parent="39" data-semantic-fencepointer="30"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="34" data-semantic-children="33" data-semantic-content="27,30" data-semantic-parent="32"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="27" data-semantic-parent="34">(</mo> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="33" data-semantic-children="29" data-semantic-content="28" data-semantic-parent="34"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="28" data-semantic-parent="33" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="29" data-semantic-parent="33">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="30" data-semantic-parent="34">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="31" data-semantic-parent="32">k</mi> </mrow> </msup> </mrow> <mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="38" data-semantic-children="35,37" data-semantic-content="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="38">k</mi> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="36" data-semantic-parent="38" data-semantic-operator="infixop,+">+</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="37" data-semantic-parent="38">z</mi> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <annotation encoding="application/x-tex">\psi \left({\frac {z+1}{2}}\right)-\psi \left({\frac {z}{2}}\right)=2\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{k+z}}</annotation> </semantics> </math>