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Display information for equation id:math.1439.270 on revision:1439
* Page found: Elektromagnetische Wellen (eq math.1439.270)
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Hash: cf24432b5d60a3acdf11b7e4d0a2cad3
TeX (original user input):
\begin{align}
& \Rightarrow \Phi \left( \bar{r}\acute{\ } \right)=C\int_{-d/2}^{d/2}{d{{s}_{1}}}{{e}^{ik\alpha {{s}_{1}}}} \\
& \alpha :=\sin {{\vartheta }_{0}} \\
& \bar{\alpha }\bar{s}={{s}_{1}}\sin {{\vartheta }_{0}} \\
& \Rightarrow \Phi \left( \bar{r}\acute{\ } \right)=\frac{C}{ik\alpha }\left( {{e}^{ik\alpha \frac{d}{2}}}-{{e}^{-ik\alpha \frac{d}{2}}} \right) \\
& \Phi \left( \bar{r}\acute{\ } \right)=Cd\frac{\sin \left( k\alpha \frac{d}{2} \right)}{k\alpha \frac{d}{2}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\Rightarrow \Phi \left({\bar {r}}{\acute {\ }}\right)=C\int _{-d/2}^{d/2}{d{{s}_{1}}}{{e}^{ik\alpha {{s}_{1}}}}\\&\alpha :=\sin {{\vartheta }_{0}}\\&{\bar {\alpha }}{\bar {s}}={{s}_{1}}\sin {{\vartheta }_{0}}\\&\Rightarrow \Phi \left({\bar {r}}{\acute {\ }}\right)={\frac {C}{ik\alpha }}\left({{e}^{ik\alpha {\frac {d}{2}}}}-{{e}^{-ik\alpha {\frac {d}{2}}}}\right)\\&\Phi \left({\bar {r}}{\acute {\ }}\right)=Cd{\frac {\sin \left(k\alpha {\frac {d}{2}}\right)}{k\alpha {\frac {d}{2}}}}\\\end{aligned}}
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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"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>Φ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mi>C</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>d</mi><mo lspace="0" rspace="0">/</mo><mn>2</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mo lspace="0" rspace="0">/</mo><mn>2</mn></mrow></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>d</mi><msub><mi>s</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>α</mi><msub><mi>s</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>α</mi><mo stretchy="false">:=</mo><mi>sin</mi><mo>⁡</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>α</mi><mo>¯</mo></mover><mover><mi>s</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><msub><mi>s</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>sin</mi><mo>⁡</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>Φ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>C</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>α</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>α</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></mrow></msup><mo stretchy="false">−</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>i</mi><mi>k</mi><mi>α</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>Φ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mi>C</mi><mi>d</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>sin</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>k</mi><mi>α</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>α</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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