Merge pull request #2070 from expikr/testbook-add-mathajx-tests

Added missing tests for MathJax to the test book

Author: ehuss

test_book/src/SUMMARY.md

@@ -22,6 +22,7 @@
   - [Tables](individual/table.md)
   - [Tasks](individual/task.md)
   - [Strikethrough](individual/strikethrough.md)
+  - [MathJax](individual/mathjax.md)
   - [Mixed](individual/mixed.md)
 - [Languages](languages/README.md)
   - [Syntax Highlight](languages/highlight.md)

test_book/src/individual/mathjax.md

@@ -0,0 +1,42 @@
+# MathJax
+
+Fourier Transform
+
+\\[
+\begin{aligned}
+f(x) &= \int_{-\infty}^{\infty}F(s)(-1)^{ 2xs}ds \\\\
+F(s) &= \int_{-\infty}^{\infty}f(x)(-1)^{-2xs}dx
+\end{aligned}
+\\]
+
+The kernel can also be written as \\(e^{2i\pi xs}\\) which is more frequently used in literature.
+
+> Proof that \\(e^{ix} = \cos x + i\sin x\\) a.k.a Euler's Formula:
+>
+> \\(
+\begin{aligned}
+  e^x &= \sum_{n=0}^\infty \frac{x^n}{n!} \implies e^{ix} = \sum_{n=0}^\infty \frac{(ix)^n}{n!} \\\\
+  \cos x &= \sum_{m=0}^\infty \frac{(-1)^m x^{2m}}{(2m)!} = \sum_{m=0}^\infty \frac{(ix)^{2m}}{(2m)!} \\\\
+  \sin x &= \sum_{s=0}^\infty \frac{(-1)^s x^{2s+1}}{(2s+1)!} = \sum_{s=0}^\infty \frac{(ix)^{2s+1}}{i(2s+1)!} \\\\
+  \cos x + i\sin x &= \sum_{l=0}^\infty \frac{(ix)^{2l}}{(2l)!} + \sum_{s=0}^\infty \frac{(ix)^{2s+1}}{(2s+1)!} = \sum_{n=0}^\infty \frac{(ix)^{n}}{n!} \\\\
+         &= e^{ix}
+\end{aligned}
+\\)
+>
+
+
+Pauli Matrices
+
+\\[
+\begin{aligned}
+  \sigma_x &= \begin{pmatrix}
+  1 & 0 \\\\ 0 & 1
+  \end{pmatrix} \\\\
+  \sigma_y &= \begin{pmatrix}
+  0 & -i \\\\ i & 0
+  \end{pmatrix} \\\\
+  \sigma_z &= \begin{pmatrix}
+  1 & 0 \\\\ 0 & -1
+  \end{pmatrix}
+\end{aligned}
+\\]