data/mathoid/172.mml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="sans-serif upper Q Subscript n Baseline left-parenthesis cosine theta right-parenthesis equals StartFraction 2 Superscript 2 n plus 1 Baseline left-parenthesis n factorial right-parenthesis squared Over left-parenthesis 2 n plus 1 right-parenthesis factorial EndFraction sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts StartFraction 1 dot 3 ellipsis left-parenthesis 2 k minus 1 right-parenthesis Over k factorial EndFraction StartFraction left-parenthesis n plus 1 right-parenthesis left-parenthesis n plus 2 right-parenthesis ellipsis left-parenthesis n plus k right-parenthesis Over left-parenthesis 2 n plus 3 right-parenthesis left-parenthesis 2 n plus 5 right-parenthesis ellipsis left-parenthesis 2 n plus 2 k plus 1 right-parenthesis EndFraction cosine left-parenthesis left-parenthesis n plus 2 k plus 1 right-parenthesis theta right-parenthesis">
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="51" data-semantic-parent="68">1</mn>
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="106" data-semantic-parent="126">2</mn>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="107" data-semantic-parent="126">n</mi>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="108" data-semantic-parent="127" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="109" data-semantic-parent="127">5</mn>
</mrow>
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</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="136" data-semantic-parent="138" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mo data-semantic-type="punctuation" data-semantic-role="ellipsis" data-semantic-id="111" data-semantic-parent="138">⋯
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</mo>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="137" data-semantic-parent="138" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="134" data-semantic-children="133" data-semantic-content="112,120" data-semantic-parent="138">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="112" data-semantic-parent="134" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="133" data-semantic-children="130,132,119" data-semantic-content="115,118" data-semantic-parent="134">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="130" data-semantic-children="113,114" data-semantic-content="129" data-semantic-parent="133">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="113" data-semantic-parent="130">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="129" data-semantic-parent="130" 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="114" data-semantic-parent="130">n</mi>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="115" data-semantic-parent="133" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="132" data-semantic-children="116,117" data-semantic-content="131" data-semantic-parent="133">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="116" data-semantic-parent="132">2</mn>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="117" data-semantic-parent="132">k</mi>
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<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="118" data-semantic-parent="133" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="119" data-semantic-parent="133">1</mn>
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</mrow>
</mfrac>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="163" data-semantic-parent="164" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="appl" data-semantic-role="prefix function" data-semantic-id="161" data-semantic-children="140,159" data-semantic-content="160,140" data-semantic-parent="164">
<mi data-semantic-type="function" data-semantic-role="prefix function" data-semantic-font="normal" data-semantic-id="140" data-semantic-parent="161" data-semantic-operator="appl">cos</mi>
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<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="159" data-semantic-children="157" data-semantic-content="142,158" data-semantic-parent="161">
<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="142" data-semantic-parent="159" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="157" data-semantic-children="155,151" data-semantic-content="156" data-semantic-parent="159">
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="155" data-semantic-children="154" data-semantic-content="143,150" data-semantic-parent="157">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="143" data-semantic-parent="155" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="154" data-semantic-children="144,153,149" data-semantic-content="145,148" data-semantic-parent="155">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="144" data-semantic-parent="154">n</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="145" data-semantic-parent="154" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="153" data-semantic-children="146,147" data-semantic-content="152" data-semantic-parent="154">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="146" data-semantic-parent="153">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="152" data-semantic-parent="153" 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="147" data-semantic-parent="153">k</mi>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="148" data-semantic-parent="154" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="149" data-semantic-parent="154">1</mn>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="150" data-semantic-parent="155" data-semantic-operator="fenced">)</mo>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="156" data-semantic-parent="157" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="151" data-semantic-parent="157">θ
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</mi>
</mrow>
<mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="158" data-semantic-parent="159" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
<annotation encoding="application/x-tex">{\mathsf {Q}}_{n}\left(\cos \theta \right)={\frac {2^{2n+1}(n!)^{2}}{(2n+1)!}}\sum _{k=0}^{\infty }{\frac {1\cdot 3\cdots (2k-1)}{k!}}{\frac {(n+1)(n+2)\cdots (n+k)}{(2n+3)(2n+5)\cdots (2n+2k+1)}}\cos \left((n+2k+1)\theta \right)</annotation>
</semantics>
</math>