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