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Display information for equation id:math.2509.16 on revision:2509
* Page found: Reale Gase (eq math.2509.16)
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Hash: 2df47201d8c9413e7d918cdccb35b0be
TeX (original user input):
\frac{4\pi \beta }{3}\int_{0}^{\infty }{{}}\left( \frac{\partial \phi }{\partial r}r \right){{e}^{-\beta \phi (r)}}{{r}^{2}}dr\tilde{\ }\left\langle \left( \frac{\partial \phi }{\partial r}r \right) \right\rangle
TeX (checked):
{\frac {4\pi \beta }{3}}\int _{0}^{\infty }{}\left({\frac {\partial \phi }{\partial r}}r\right){{e}^{-\beta \phi (r)}}{{r}^{2}}dr{\tilde {\ }}\left\langle \left({\frac {\partial \phi }{\partial r}}r\right)\right\rangle
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MathML (1.884 KB / 428 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi><mi>β</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϕ</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>r</mi></mrow></mrow></mfrac></mrow><mi>r</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>β</mi><mi>ϕ</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></mrow></msup><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>d</mi><mi>r</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϕ</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>r</mi></mrow></mrow></mfrac></mrow><mi>r</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mstyle></mrow></math>
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