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Latex/Mathjax (test article)

Testing MathJax/Katex for mathematical syntax

Let $n$ be a natural number, and define $m := n^2 + 1$. Then

$$ \frac{1}{\Gamma(s)}\int_{0}^{\infty}\frac{u^{s-1}}{e^{u}-1}\mathrm{d}u $$

$$ \begin{bmatrix} a_{1,1} & a_{1,2} & … & a_{1,n} & \mid b_1\\
a_{2,1} & a_{2,2} & … & a_{2,n} & \mid b_2\\
\vdots\\
a_{m,1} & 1_{m,2} & … & a_{m,n} & \mid b_m \end{bmatrix} $$

$$ \begin{array} {lcl} L(p,w_i) &=& \dfrac{1}{N}\Sigma_{i=1}^N(\underbrace{f_r(x_2 \rightarrow x_1 \rightarrow x_0)G(x_1 \longleftrightarrow x_2)f_r(x_3 \rightarrow x_2 \rightarrow x_1)}_{sample, radiance, evaluation, in, stage2} \\\ &=& \prod_{i=3}^{k-1}(\underbrace{\dfrac{f_r(x_{i+1} \rightarrow x_i \rightarrow x_{i-1})G(x_i \longleftrightarrow x_{i-1})}{p_a(x_{i-1})}}_{stored,in,vertex, during,light, path, tracing, in, stage1})\dfrac{G(x_k \longleftrightarrow x_{k-1})L_e(x_k \rightarrow x_{k-1})}{p_a(x_{k-1})p_a(x_k)}) \end{array} $$