Differentials
\bigg(\frac{\partial^2} {\partial x^2} + \frac {\partial^2}{\partial y^2} \bigg){\big\lvert\varphi (x+iy)\big\rvert}^2	$$(\frac{{\partial }^2}{\partial x^2}+\frac{{\partial }^2}{\partial y^2}){|\phi (x+iy)|}^2$$
Environments
f(x) = \begin{cases}1/3 & \text{if }0 \le x \le 1; \\ 2/3 & \text{if }3\le x \le 4;\\ 0 &\text{elsewhere.} \end{cases}	$$f(x)=\{\begin{array}{cc}1/3& \text{if }0\le x\le 1;\\ 2/3& \text{if }3\le x\le 4;\\ 0& \text{elsewhere.}\end{array}$$
\begin{pmatrix} \begin{pmatrix}a&b\\c&d \end{pmatrix} & \begin{pmatrix}e&f\\g&h \end{pmatrix} \\ 0 & \begin{pmatrix}i&j\\k&l \end{pmatrix} \end{pmatrix}	$$\left(\begin{array}{cc}\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)& \left(\begin{array}{cc}e& f\\ g& h\end{array}\right)\\ 0& \left(\begin{array}{cc}i& j\\ k& l\end{array}\right)\end{array}\right)$$
\det\begin{vmatrix} c_0&c_1&c_2&\dots& c_n\\ c_1 & c_2 & c_3 & \dots & c_{n+1}\\ c_2 & c_3 & c_4 &\dots & c_{n+2}\\ \vdots &\vdots&\vdots & &\vdots \\c_n & c_{n+1} & c_{n+2} &\dots&c_{2n} \end{vmatrix} > 0	$$\det \left|\begin{array}{ccccc}{c}_0& c_1& c_2& \cdots & c_n\\ c_1& c_2& c_3& \cdots & c_{n+1}\\ c_2& c_3& c_4& \cdots & c_{n+2}\\ ⋮& ⋮& ⋮& & ⋮\\ c_n& c_{n+1}& c_{n+2}& \cdots & c_{2n}\end{array}\right|>0$$
Everything
\sum_{p\text{ prime}} f(p)=\int_{t>1} f(t)d\pi(t)	$$\sum _{p\text{ prime}}f(p)={\int }_{t>1}f(t)d\pi (t)$$
\lim_{n \to +\infty} \frac{\sqrt{2\pi n}}{n!} \genfrac (){}{}n{e}^n = 1	$$\underset{n\to +\infty }{\lim }\frac{\sqrt{2\pi n}}{n!}{\left(\frac{n}{e}\right)}^n=1$$
\det(A) = \sum_{\sigma \in S_n} \epsilon(\sigma) \prod_{i=1}^n a_{i, \sigma_i}	$$\det (A)=\sum _{\sigma \in S_n}ϵ(\sigma )\prod _{i=1}^n{a}_{i,{\sigma }_i}$$
Fractions
\frac{x+y^2}{k+1}	$$\frac{x+y^2}{k+1}$$
x+y^\frac{2}{k + 1}	$$x+y^{\frac{2}{k+1}}$$
\frac{a}{b/2}	$$\frac{a}{b/2}$$
a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4}}}}	$$a_0+\frac{1}{a_1+\frac{1}{a_2+\frac{1}{a_3+\frac{1}{a_4}}}}$$
a_0+\frac{1}{a_1+\frac{1}{a_2+\frac{1}{a_3+ \frac{1}{a_4}}}}	$$a_0+\frac{1}{a_1+\frac{1}{a_2+\frac{1}{a_3+\frac{1}{a_4}}}}$$
\binom{p}{2} x^2 y^{p-2} - \frac{1}{1-x} \frac{1}{1-x^2}	$$\left(\genfrac{}{}{0em}{}{p}{2}\right)x^2{y}^{p-2}-\frac{1}{1-x}\frac{1}{1-x^2}$$
Integrals
\int_1^x \frac{dt}{t}	$${\int }_1^x\frac{dt}{t}$$
\int\!\!\!\int_D dx,dy	$$\int {\int }_{D}dx,dy$$
Over Under Braces
\overbrace{x +\cdots + x} ^{k \text{ times}}	$$\stackrel{k\text{ times}}{\overbrace{x+\cdots +x}}$$
{\underbrace{\overbrace{ \mathstrut a,\dots,a}^{k ,a\rq\text{s}}, \overbrace{ \mathstrut b,\dots,b}^{l, b\rq\text{s}}}_{k+l \text{ elements}}}	$$\underset{k+l\text{ elements}}{\underbrace{\stackrel{k,a\prime \text{s}}{\overbrace{height="0.7em"\; />a,\dots ,a}},\stackrel{l,b\prime \text{s}}{\overbrace{height="0.7em"\; />b,\dots ,b}}}}$$
Roots
\sqrt{1+\sqrt{1+\sqrt{1+ \sqrt{1+\sqrt{1+\sqrt{1+ \sqrt{1+x}}}}}}}	$$\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+x}}}}}}}$$
Scripts
x^2y^2	$$x^2{y}^2$$
_2F_3	$${}_2{F}_3$$
x^{2y}	$$x^{2y}$$
2^{2^{2^x}}	$$2^{2^{2^x}}$$
y_{x^2}	$$y_{x^2}$$
y_{x_2}	$$y_{x_2}$$
x_{92}^{31415} + \pi	$$x_{92}^{31415}+\pi$$
x_{y^a_b}^{z^c_d}	$$x_{y_b^a}^{z_d^c}$$
y_3'''	$$y_3\prime \prime \prime$$
Summations
\sum_{\genfrac{}{}{0mu}{2}{0 \le i \le m}{0 < j < n}} P(i, j)	$$\sum _{\genfrac{}{}{0mu}{}{0\le i\le m}{0<j<n}}P(i,j)$$
\sum_{i=1}^p \sum_{j=1}^q \sum_{k=1}^r a_{ij}b_{jk}c_{ki}	$$\sum _{i=1}^p\sum _{j=1}^q\sum _{k=1}^r{a}_{ij}{b}_{jk}{c}_{ki}$$