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Mathjax: \( f{(a)}=\frac1{2\pi i}\oint_\gamma\frac{f(z)}{z-a}dz \)
Mathjax: \( x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \)
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
$$\left [ – \frac{\hbar^2}{2 m} \frac{\partial^2}{\partial x^2} + V \right ] \Psi = i \hbar \frac{\partial}{\partial t} \Psi$$
The Lorenz Equations
$$\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x – y – xz \\
\dot{z} & = -\beta z + xy
\end{align}
$$
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The Cauchy-Schwarz Inequality
$$ \left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$
$$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}.$$
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