\(\)
Install and run on Ubuntu (OSX and Windows supported too):
sudo snap install mathpix-snipping-tool mathpix-snipping-toolIf you know how to install a snap on a IT-managed desktop machine talk to me! I stopped after 2+ hours going nowhere ...
\[
\begin{aligned} \mathbb{E}\left[\frac{1}{n} \sum_{i} f_{i}\left(\phi_{i}^{k+1}\right)\right] &=\frac{1}{n} f\left(x^{k}\right)+\left(1-\frac{1}{n}\right) \frac{1}{n} \sum_{i} f_{i}\left(\phi_{i}^{k}\right) \\ \mathbb{E}\left[-\frac{1}{n} \sum_{i}\left\langle f_{i}^{\prime}\left(x^{*}\right), \phi_{i}^{k+1}-x^{*}\right\rangle\right] &=-\frac{1}{n}\left\langle f^{\prime}\left(x^{*}\right), x^{k}-x^{*}\right\rangle-\left(1-\frac{1}{n}\right) \frac{1}{n} \sum_{i}\left\langle f_{i}^{\prime}\left(x^{*}\right), \phi_{i}^{k}-x^{*}\right\rangle \end{aligned}
\]
\[
\begin{array}{l}{\boldsymbol{R} \mathscr{J}_{n}=\exp (i \phi)\left(-\frac{i}{r} \frac{\partial}{\partial \phi}-\frac{\partial}{\partial r}\right) \mathscr{J}_{n}=\mathscr{J}_{n+1}} \\ {\mathcal{L} \mathscr{J}_{n}=\exp (-i \phi)\left(-\frac{i}{r} \frac{\partial}{\partial \phi}+\frac{\partial}{\partial r}\right) \mathscr{J}_{n}=\mathscr{J}_{n-1}}\end{array}
\]
\[
\begin{array}{l}
{\nabla \cdot E=\frac{f}{\varepsilon_{0}}} \\
{\nabla \cdot B=0} \\ {\nabla \times E=-\frac{\partial B}{\partial t}} \\
{\nabla \times B=\mu_{0} J+\mu_{0} \varepsilon_{0} \frac{\partial E}{\partial t}}
\end{array}
\]