image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1 value | data_type stringclasses 1 value |
|---|---|---|---|---|
\frac{1}{(4\pi it)^{n/2}}e^{i|x|^{2}/4t} | fb64cf4d4a814233 | train | human | |
\frac{-3*-3*2}{(2+3x)^{3}} | dbd47b5a1c5fffad | train | human | |
{78^{5}}^{26-\sqrt{9}+\sqrt{360}} | ae6e84e1a8ca9889 | train | human | |
\hat{Z} | 30de262278179338 | train | human | |
t_{1/2}=\frac{ln(2)}{k} | b53d2631a97449b5 | train | human | |
\frac{3+103^{285}}{141^{295}} | 56eaaf56177f9994 | train | human | |
\frac{1\cdot394^{5}}{\frac{\frac{7}{272}}{177}} | 35f3bd7d830b13c1 | train | human | |
\frac{a^{x}\Gamma(\frac{ax+b}{a})}{\Gamma(\frac{a+b}{a})} | aca9057d7fb02c33 | train | human | |
\int_{\infty}^{\infty} | 8cd4b708ac789f03 | train | human | |
2^{10/12}=\sqrt[6]{32} | c2666b1add2e7603 | train | human | |
\frac{1}{\sqrt{n!}}\le\frac{1}{2^{n}} | e63ade4e05fbda09 | train | human | |
\sqrt{h_{1}^{2}+h_{2}^{2}} | 0b516fb2c46169ad | train | human | |
\sum_{i=1}^{n}\frac{n(n+1)}{2} | 08aee38a42a3d27d | train | human | |
\frac{(\frac{493}{8})^{470}}{\frac{31}{4}} | b88eb6b2c8abfa4a | train | human | |
a/b=2^{n} | 66672621f9105d09 | train | human | |
\theta^{\omega_{8}} | 55e435fb0dee5991 | train | human | |
[z^{2n}][u]g(z,u) | 2efb6754dbe2fccd | train | human | |
k^{2}=1-\frac{\mu}{h^{2}} | 7d5c6d65181afd30 | train | human | |
((\frac{442}{\sqrt{389}})^{8})^{395^{1}} | 80df9ad2e48d98d5 | train | human | |
\tilde{e}_{i}\tilde{f}_{i} | bd629fe2e12205ea | train | human | |
lim_{t\rightarrow\infty}T^{t} | 6669c79d4d1e16e6 | train | human | |
E_{X}=\frac{RT}{zF}ln\frac{X_{o}}{X_{i}} | d470a851fdee691b | train | human | |
\frac{h-y}{h} | c53764568418d528 | train | human | |
F[y]=\int_{E}ytdt | 6c0efad84500a9ab | train | human | |
\tilde{P}(q,\omega) | b106b3d737a85927 | train | human | |
2T=\sum_{ij}g_{ij}\dot{s}_{i}\dot{s}_{j} | 32467aee9100d38e | train | human | |
\frac{M-\lambda}{2} | 66d8090ed98116af | train | human | |
F(x;2)=1-e^{-\frac{x}{2}} | edabad811577d98f | train | human | |
\int\Delta f=0 | 18f0df3a76d939ad | train | human | |
\tilde{F}_{4} | 83ee3144f8094010 | train | human | |
11^{7-j} | 3267b5e28587fef3 | train | human | |
\frac{T}{P}=\frac{x_{p}-x_{f}}{x_{f}-x_{t}} | 62adf6eac391482a | train | human | |
\overline{A}=\{x|x\notin A\} | 9f9ee0a07df13c43 | train | human | |
\delta\int2T(t)dt=0 | 9d39e4074be7f73c | train | human | |
r^{(\frac{\epsilon}{\mu})[4\cdot\sqrt{4\cdot\frac{2\mu^{2}t}{\epsilon}}]} | ffb1d4356d8ceccf | train | human | |
E[F|x^{(t)}] | 5c86ba09a7c1e222 | train | human | |
\frac{A}{B}\times\frac{C}{D} | 96b8b88151535c8b | train | human | |
p=\frac{m_{8}f}{\sqrt{5-\frac{f^{2}}{n^{2}}}} | ea928fbcc743b1d1 | train | human | |
=12.250(121/4) | 59514ecac5e1764c | train | human | |
\varphi(\xi)=arg(\hat{f}(\xi)) | 16d4c9f6d1f965e7 | train | human | |
\frac{L}{t}=(\frac{l}{t})(\frac{180}{\pi\theta}) | ebb007df0f4fb380 | train | human | |
\frac{dx}{dt}=r\pm x^{2} | 78db3231db0681d5 | train | human | |
(\begin{matrix}U_{1}\\ U_{2}\end{matrix}) | ce805426e18f3d28 | train | human | |
\frac{7^{190}}{\sqrt{4}/8} | a191fb9a1ce3f0ae | train | human | |
sqrt-1 | 07e641c472ba1ecf | train | human | |
\frac{dP}{dx} | 175c60fea52adfad | train | human | |
\frac{\frac{9}{160}}{323^{339}\cdot\sqrt{383}} | 12f52f3585214183 | train | human | |
\frac{\frac{2}{3}}{{8^{6}}^{6}} | 8a10a9d8df9a75ad | train | human | |
y=x^{2}\iff x=\sqrt{y} | b298b451018dcec8 | train | human | |
2(\sqrt{2}-1)\approx0.828 | 8d58aceefea81ae3 | train | human | |
\int_{1}^{a}\frac{1}{x}dx=lna | a74bfc27ed6bb6a6 | train | human | |
\hat{e}_{j} | 97119cdcc0d87756 | train | human | |
p_{cv}(t)\propto e^{-i\Delta\epsilon t/\hbar} | 036ac8e0f2aa8561 | train | human | |
\frac{dL}{dt}=-k_{r}L | 50fea80986d267db | train | human | |
(|S|-1) | b2573b0c4d4226b4 | train | human | |
p\notin f(\partial\Omega) | 2b6aa8aff329a271 | train | human | |
(\begin{matrix}21\end{matrix})(\begin{matrix}21\end{matrix})(\begin{matrix}31\end{matrix})(\begin{matrix}401\end{matrix}) | 18c42c04d222d6ea | train | human | |
-z^{2}+1 | c21dc85c70e7f9df | train | human | |
\int_{0}^{1}g_{n}=1 | 3fd9cf0612d9ff1c | train | human | |
(\begin{matrix}m\\ 2\end{matrix}) | beec97e9d0019c82 | train | human | |
(\begin{matrix}n\\ 2k\end{matrix}) | a36cc6f4f40fa54c | train | human | |
(\begin{matrix}8\\ 1\end{matrix}) | 3353dd2569e31349 | train | human | |
1-\frac{2}{\sqrt{5}} | 4f47b6b03e655df9 | train | human | |
\tilde{\chi} | d88039c022aa35a8 | train | human | |
\int_{0}^{\infty}\frac{n^{\cdot(\frac{(y+z)^{8}}{8w})}}{\sqrt{8\mu w}} | 9b2644dc85d044df | train | human | |
(\begin{matrix}5\\ 5\end{matrix}) | 948a7fbb8c9e94df | train | human | |
N_{b}^{r} | 97922b013225709a | train | human | |
\frac{c\Delta t}{2} | 8d096918bdadf9db | train | human | |
y=\int\frac{dy}{dx}dx | 682c3af34d196843 | train | human | |
\frac{7v^{-\frac{1}{x^{7}}}}{x^{4}} | 4b4aad8cc40178d0 | train | human | |
\hat{D_{B}} | 2135bbaee4fe4f9d | train | human | |
sinhx=\frac{e^{x}-e^{-x}}{2} | 56acdeed684cd298 | train | human | |
\hat{\alpha}=[\begin{matrix}\alpha&0&0\\ 0&\alpha&0\\ 0&0&\alpha\end{matrix}] | 7ff8f4da51812e89 | train | human | |
\int f(t)dt=0 | 4c508c2173cdde78 | train | human | |
\frac{\partial S}{\partial x_{i}} | 6119448bb5206d1d | train | human | |
x\notin\{y:d(x,y)>r\} | b9e88310ed90cde9 | train | human | |
\hat{p}_{o} | 6a923617a2adfe8c | train | human | |
V=-\frac{1}{2}{\eta_{1}}^{-1} | 070959d4a4028441 | train | human | |
||\alpha|| | d95e2b07215094f0 | train | human | |
M_{i}v_{i,s}^{2}/2=eZ_{i}U_{g} | 77507d5eabebf393 | train | human | |
\hat{X_{a}} | f364249bdb05cbe9 | train | human | |
u^{u^{\cdot^{\cdot^{u^{e}}}}} | 44462f61d3b9b356 | train | human | |
4^{\sqrt{8}}+10-\frac{10}{9}-8 | f2e45b74bcd94236 | train | human | |
(\frac{\frac{10}{10}}{118})^{3^{\sqrt{10}}} | 3b2e6e56f75ed27b | train | human | |
M=B\frac{d^{2}\theta}{dt^{2}} | 2ec76a9c191edf5a | train | human | |
[.,.]_{A} | 8a4a5ce8f0efd189 | train | human | |
\hat{\eta} | 2880faf2a7a95987 | train | human | |
\frac{\partial\Psi}{\partial J} | f047f0e5da0315f4 | train | human | |
(\begin{matrix}p\\ i\end{matrix}) | 5ffde63799a07fc8 | train | human | |
\tau(X,X^{\prime}) | ac932eac84ea5337 | train | human | |
Im\cdot exp(\frac{2mc^{2}}{mv^{2}}) | 8567e6b1a92f2a23 | train | human | |
s_{i}=\lceil-log_{a}p_{i}\rceil | 77cec87097035460 | train | human | |
{410^{\sqrt{122}}/308}^{\frac{(70/10)}{3}} | 22851edfd057fbed | train | human | |
F(x)=\int_{x}^{0}f(y)dy | 8d5abe86e577b366 | train | human | |
\int_{0}^{\infty}\frac{s^{-(\frac{(y+j)^{1}}{1l})}}{\sqrt{1\omega l}} | 8cecc2b29bf03817 | train | human | |
\int_{0}^{1}f(x)dx | 40a214dcb6d9c5ae | train | human | |
x,y\in\mathbb{Z}+\mathbb{Z}\sqrt{10} | 91d8aba64e94b7b3 | train | human | |
det[\begin{matrix}1&-1\\ 1&2\end{matrix}]=3\ne0 | 641aba136affdde5 | train | human | |
\overline{X_{t}}=X_{t}=\emptyset | 3e7a53d217b46781 | train | human | |
(\begin{matrix}p+q+3\\ 2\end{matrix}) | 9ed53fbabca813b3 | train | human |
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