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Display information for equation id:math.1669.24 on revision:1669
* Page found: Ortsdarstellung des Bahndrehimpulses (eq math.1669.24)
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Hash: d2095134fbc9d216a2e8085982cd1c61
TeX (original user input):
\int\limits_{0}^{2\pi }{d\phi \int\limits_{0}^{\pi }{d\vartheta \sin \vartheta }}{{\left[ {{Y}_{l}}^{m}(\vartheta ,\phi ) \right]}^{*}}{{Y}_{l\acute{\ }}}^{m\acute{\ }}(\vartheta ,\phi )={{\delta }_{ll\acute{\ }}}{{\delta }_{mm\acute{\ }}}
TeX (checked):
\int \limits _{0}^{2\pi }{d\phi \int \limits _{0}^{\pi }{d\vartheta \sin \vartheta }}{{\left[{{Y}_{l}}^{m}(\vartheta ,\phi )\right]}^{*}}{{Y}_{l{\acute {\ }}}}^{m{\acute {\ }}}(\vartheta ,\phi )={{\delta }_{ll{\acute {\ }}}}{{\delta }_{mm{\acute {\ }}}}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><munderover><mo form="prefix" stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></mrow></munderover><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ϕ</mi><munderover><mo form="prefix" stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ϑ</mi><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi></mrow></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><msub><mi>Y</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mo stretchy="false">(</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">∗</mo></mrow></msup><msup><msub><mi>Y</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>l</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msup><mo stretchy="false">(</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>l</mi><mi>l</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msub><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mi>m</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msub></mstyle></mrow></math>
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