User:DeanFerreyra/Sandbox

${\sqrt {1-e^{2}}}$

$P(E)={n \choose k}p^{k}(1-p)^{n-k}$

$\left(\sum _{k=1}^{n}a_{k}b_{k}\right)^{2}\leq \left(\sum _{k=1}^{n}a_{k}^{2}\right)\left(\sum _{k=1}^{n}b_{k}^{2}\right)$

${\begin{aligned}{\dot {x}}&=\sigma (y-x)\\{\dot {y}}&=\rho x-y-xz\\{\dot {z}}&=-\beta z+xy\end{aligned}}\,\!$

${\begin{aligned}\nabla \times {\vec {\mathbf {B} }}-\,{\frac {1}{c}}\,{\frac {\partial {\vec {\mathbf {E} }}}{\partial t}}&={\frac {4\pi }{c}}{\vec {\mathbf {j} }}\\\nabla \cdot {\vec {\mathbf {E} }}&=4\pi \rho \\\nabla \times {\vec {\mathbf {E} }}\,+\,{\frac {1}{c}}\,{\frac {\partial {\vec {\mathbf {B} }}}{\partial t}}&={\vec {\mathbf {0} }}\\\nabla \cdot {\vec {\mathbf {B} }}&=0\end{aligned}}\,\!$

${\frac {1}{{\Bigl (}{\sqrt {\phi {\sqrt {5}}}}-\phi {\Bigr )}e^{{\frac {2}{5}}\pi }}}=1+{\frac {e^{-2\pi }}{1+{\frac {e^{-4\pi }}{1+{\frac {e^{-6\pi }}{1+{\frac {e^{-8\pi }}{1+\ldots }}}}}}}}\,\!$

$\mathbf {V} _{1}\times \mathbf {V} _{2}={\begin{vmatrix}\mathbf {i} &\mathbf {j} &\mathbf {k} \\{\frac {\partial X}{\partial u}}&{\frac {\partial Y}{\partial u}}&0\\{\frac {\partial X}{\partial v}}&{\frac {\partial Y}{\partial v}}&0\end{vmatrix}}\,\!$