Add MathJax tests.
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- [Tables](individual/table.md)
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- [Tables](individual/table.md)
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- [Tasks](individual/task.md)
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- [Tasks](individual/task.md)
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- [Strikethrough](individual/strikethrough.md)
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- [Strikethrough](individual/strikethrough.md)
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- [MathJax](individual/mathjax.md)
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- [Mixed](individual/mixed.md)
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- [Mixed](individual/mixed.md)
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- [Languages](languages/README.md)
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- [Languages](languages/README.md)
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- [Syntax Highlight](languages/highlight.md)
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- [Syntax Highlight](languages/highlight.md)
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# MathJax
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Fourier Transform
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\\[
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\begin{aligned}
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f(x) &= \int_{-\infty}^{\infty}F(s)(-1)^{ 2xs}ds \\\\
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F(s) &= \int_{-\infty}^{\infty}f(x)(-1)^{-2xs}dx
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\end{aligned}
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\\]
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The kernel can also be written as \\(e^{2i\pi xs}\\) which is more frequently used in literature.
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> Proof that \\(e^{ix} = \cos x + i\sin x\\) a.k.a Euler's Formula:
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>
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> \\(
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\begin{aligned}
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e^x &= \sum_{n=0}^\infty \frac{x^n}{n!} \implies e^{ix} = \sum_{n=0}^\infty \frac{(ix)^n}{n!} \\\\
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\cos x &= \sum_{m=0}^\infty \frac{(-1)^m x^{2m}}{(2m)!} = \sum_{m=0}^\infty \frac{(ix)^{2m}}{(2m)!} \\\\
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\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)!} \\\\
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\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!} \\\\
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&= e^{ix}
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\end{aligned}
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\\)
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>
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Pauli Matrices
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\\[
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\begin{aligned}
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\sigma_x &= \begin{pmatrix}
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1 & 0 \\\\ 0 & 1
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\end{pmatrix} \\\\
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\sigma_y &= \begin{pmatrix}
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0 & -i \\\\ i & 0
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\end{pmatrix} \\\\
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\sigma_z &= \begin{pmatrix}
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1 & 0 \\\\ 0 & -1
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\end{pmatrix}
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\end{aligned}
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\\]
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