mathmlben
Version:
Visualization for goldstandard
137 lines • 14 kB
text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="StartFraction normal d squared w Over normal d z prime squared EndFraction plus left-parenthesis h prime minus nu left-parenthesis nu plus 1 right-parenthesis k prime squared s n squared left-parenthesis z prime comma k Superscript prime Baseline right-parenthesis right-parenthesis w equals 0">
<semantics>
<mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="62" data-semantic-children="61,49" data-semantic-content="48">
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="61" data-semantic-children="14,60" data-semantic-content="15" data-semantic-parent="62">
<mrow class="MJX-TeXAtom-ORD">
<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="14" data-semantic-children="5,13" data-semantic-parent="61">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="5" data-semantic-children="2,3" data-semantic-content="4" data-semantic-parent="14">
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="2" data-semantic-children="0,1" data-semantic-parent="5">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="0" data-semantic-parent="2">d</mi>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="1" data-semantic-parent="2">2</mn>
</mrow>
</msup>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="4" data-semantic-parent="5" 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="3" data-semantic-parent="5">w</mi>
</mrow>
<msup data-semantic-type="superscript" data-semantic-role="implicit" data-semantic-id="13" data-semantic-children="11,12" data-semantic-parent="14">
<mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="11" data-semantic-children="6,9" data-semantic-content="10" data-semantic-parent="13">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="6" data-semantic-parent="11">d</mi>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="10" data-semantic-parent="11" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="9" data-semantic-children="7,8" data-semantic-parent="11">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="7" data-semantic-parent="9">z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-variant" mathvariant="normal" data-semantic-type="punctuation" data-semantic-role="prime" data-semantic-font="normal" data-semantic-id="8" data-semantic-parent="9">′
<!-- ′ -->
</mi>
</mrow>
</msup>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="12" data-semantic-parent="13">2</mn>
</mrow>
</msup>
</mfrac>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="15" data-semantic-parent="61" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="60" data-semantic-children="58,47" data-semantic-content="59" data-semantic-parent="61">
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="58" data-semantic-children="57" data-semantic-content="16,46" data-semantic-parent="60">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="16" data-semantic-parent="58" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="57" data-semantic-children="19,56" data-semantic-content="20" data-semantic-parent="58">
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="19" data-semantic-children="17,18" data-semantic-parent="57">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="17" data-semantic-parent="19">h</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-variant" mathvariant="normal" data-semantic-type="punctuation" data-semantic-role="prime" data-semantic-font="normal" data-semantic-id="18" data-semantic-parent="19">′
<!-- ′ -->
</mi>
</mrow>
</msup>
<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="20" data-semantic-parent="57" data-semantic-operator="infixop,−">−
<!-- − -->
</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="56" data-semantic-children="21,51,31,34,45" data-semantic-content="52,53,54,55" data-semantic-parent="57">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="21" data-semantic-parent="56">ν
<!-- ν -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="52" data-semantic-parent="56" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="51" data-semantic-children="50" data-semantic-content="22,26" data-semantic-parent="56">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="22" data-semantic-parent="51" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="50" data-semantic-children="23,25" data-semantic-content="24" data-semantic-parent="51">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="23" data-semantic-parent="50">ν
<!-- ν -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="24" data-semantic-parent="50" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="25" data-semantic-parent="50">1</mn>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="26" data-semantic-parent="51" data-semantic-operator="fenced">)</mo>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="53" data-semantic-parent="56" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="31" data-semantic-children="29,30" data-semantic-parent="56">
<mrow class="MJX-TeXAtom-ORD">
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="29" data-semantic-children="27,28" data-semantic-parent="31">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="27" data-semantic-parent="29">k</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-variant" mathvariant="normal" data-semantic-type="punctuation" data-semantic-role="prime" data-semantic-font="normal" data-semantic-id="28" data-semantic-parent="29">′
<!-- ′ -->
</mi>
</mrow>
</msup>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="30" data-semantic-parent="31">2</mn>
</mrow>
</msup>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="54" data-semantic-parent="56" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow class="MJX-TeXAtom-ORD">
<msup data-semantic-type="superscript" data-semantic-role="unknown" data-semantic-id="34" data-semantic-children="32,33" data-semantic-parent="56">
<mi data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="32" data-semantic-parent="34">sn</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="33" data-semantic-parent="34">2</mn>
</mrow>
</msup>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="55" data-semantic-parent="56" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="45" data-semantic-children="43" data-semantic-content="35,44" data-semantic-parent="56">
<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="35" data-semantic-parent="45" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="43" data-semantic-children="38,39,42" data-semantic-content="39" data-semantic-parent="45">
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="38" data-semantic-children="36,37" data-semantic-parent="43">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="36" data-semantic-parent="38">z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-variant" mathvariant="normal" data-semantic-type="punctuation" data-semantic-role="prime" data-semantic-font="normal" data-semantic-id="37" data-semantic-parent="38">′
<!-- ′ -->
</mi>
</mrow>
</msup>
<mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="39" data-semantic-parent="43" data-semantic-operator="punctuated">,</mo>
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="42" data-semantic-children="40,41" data-semantic-parent="43">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="40" data-semantic-parent="42">k</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-variant" mathvariant="normal" data-semantic-type="punctuation" data-semantic-role="prime" data-semantic-font="normal" data-semantic-id="41" data-semantic-parent="42">′
<!-- ′ -->
</mi>
</mrow>
</msup>
</mrow>
<mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="44" data-semantic-parent="45" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="46" data-semantic-parent="58" data-semantic-operator="fenced">)</mo>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="59" data-semantic-parent="60" 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="47" data-semantic-parent="60">w</mi>
</mrow>
</mrow>
<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="48" data-semantic-parent="62" data-semantic-operator="relseq,=">=</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="49" data-semantic-parent="62">0</mn>
</mrow>
<annotation encoding="application/x-tex">{\frac {{\mathrm {d} }^{2}w}{{\mathrm {d} z^{\prime }}^{2}}}+(h^{\prime }-\nu (\nu +1){k^{\prime }}^{2}{\operatorname {sn} ^{2}}\left(z^{\prime },k^{\prime }\right))w=0</annotation>
</semantics>
</math>