image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1 value | data_type stringclasses 1 value |
|---|---|---|---|---|
\overline{A^{2}} | cdbde961873cdb7f | train | human | |
\hat{x}=\frac{1}{N}\sum_{i=1}^{N}y_{i} | b5cdbf837334248f | train | human | |
(\frac{9}{2})^{\sqrt{129}^{\sqrt{119}}+1} | d780354405718fa2 | train | human | |
\frac{N}{t}=\frac{I}{e} | cd36612bb9f292d3 | train | human | |
=\frac{\pi^{2}}{10}-arcsch^{2}2 | 7481b93864283e59 | train | human | |
\int_{\gamma}dz=0 | 8fe01d9e8e5afdb7 | train | human | |
\int d^{4}xF(x) | 3553b6dae74f7422 | train | human | |
dw_{j}=\frac{dx_{j}v_{j}}{\sqrt{1-\frac{v_{j}^{6}}{z^{6}}}} | e72f1c10629e8c12 | train | human | |
x^{d}-1=\prod_{m|d}\Phi_{m}(x) | 1a3178cc54fe2950 | train | human | |
f,f^{\prime}\in H | 2f1a4cdc61991abd | train | human | |
S(t|\theta)=S_{0}(\theta t) | 8bc0618d1145346d | train | human | |
\frac{a}{1-a}=\frac{C_{x}\sigma_{r}}{4sin^{2}\phi} | 3f195fb1f4177a92 | train | human | |
(\frac{(7/229)}{\sqrt{2}})^{(289\cdot3)} | 91f79310607eff63 | train | human | |
372^{4}/152^{3} | 128f6701b124d8e5 | train | human | |
\lceil\frac{n^{\prime}}{k}\rceil | 1867f758ade97cd8 | train | human | |
\tilde{u}_{i} | 5fe28a2a72abca87 | train | human | |
\frac{dx}{dt}=\dot{x} | e0377f213e93ac48 | train | human | |
DSH=\frac{dv}{dx}+\frac{du}{dy} | be939cb5e0cef0d1 | train | human | |
[a,b] | f47cf4cab1c96198 | train | human | |
Q(x)=\prod_{i=1}^{k}f_{i}(x) | 77e1707af3e57a49 | train | human | |
\frac{\frac{1}{176}}{\frac{469}{10}} | 776892c32d8b870a | train | human | |
\tilde{u}_{i} | f7366d0c28b57ced | train | human | |
\frac{n!}{(n-k)!k!} | da607cae396af588 | train | human | |
\hat{x}_{2} | 093f0e1362e266ec | train | human | |
4,\frac{3\pm\sqrt{73}}{2} | 08dd3f98445f52f5 | train | human | |
2^{-r_{2}}\sqrt{|\Delta_{K}|} | 4113012eb9f71d26 | train | human | |
\sum_{1}^{k}(\frac{X_{i}-\mu_{i}}{\sigma_{i}})^{2} | f65405630373ee64 | train | human | |
\frac{q-2}{q} | b0b46a9b2f952c88 | train | human | |
\sqrt{x}=1+\frac{x-1}{1+\sqrt{x}} | acf3b544fec19f71 | train | human | |
{143^{358}}^{\frac{334-127}{209}} | 8cf5c9aeb020bbbe | train | human | |
W=\alpha M\tilde{Q^{c}}\tilde{Q} | 61acf0361ef2e312 | train | human | |
2^{2^{2^{f^{a}}}} | a0da1c0b1bac2838 | train | human | |
\overline{z} | 3dec7c902a96a07f | train | human | |
p||q=pb^{l(q)}+q | 2f739f595d98aded | train | human | |
\frac{\partial T}{\partial q_{k}} | d1ecef04249a08f3 | train | human | |
\hat{A}_{0}=1 | e3791275d4583db8 | train | human | |
m=\frac{8}{3}\cdot\frac{h\epsilon_{0}}{c^{2}} | 0999dd14463ea83d | train | human | |
\hat{p}=0 | 738c51bd5f269539 | train | human | |
(\begin{matrix}n\\ k\end{matrix}) | c2e147ee13cb5401 | train | human | |
x_{2}=b+\sqrt{b^{2}-c} | b06d3d021748cddf | train | human | |
\frac{1-m^{3}}{(m+1)^{2}}=0 | ac1210d258df65c6 | train | human | |
\lfloor\frac{13(m+1)}{5}\rfloor | 8fa832fd7d6761ba | train | human | |
\int_{X}\int_{Y}\int_{Z} | 64e1b9f2d91a9ee7 | train | human | |
\frac{323\cdot1^{6}}{(\frac{10}{388})^{1}} | 36fbd05975c5ff0b | train | human | |
\frac{12}{1+n} | 6cb6f9e9c1ea9500 | train | human | |
g<g_{safe} | b8f9fd8db1a771c0 | train | human | |
\frac{27-74}{4}\cdot\frac{8}{298} | 89e99bf93eaa8d71 | train | human | |
\frac{\alpha_{1}}{\alpha_{1}+\beta_{1}} | 5c43d7b53663e41a | train | human | |
\theta,\varphi | ab1405f68a53bf44 | train | human | |
y(x)=m(-1)^{\lfloor\nu x\rfloor} | a5e76c53834e34b2 | train | human | |
x\frac{d}{dx}(y\frac{dy}{dx}) | b97bcdb7c3a68825 | train | human | |
\overline{x} | 3bf71a4dd1ab9406 | train | human | |
(\begin{matrix}n\\ k\end{matrix})_{q} | f04bac13160f748f | train | human | |
\prod_{x}x=C\Gamma(x) | 33da2d447e98b161 | train | human | |
s=Rtan^{-1}\frac{d}{R} | 22eeb9b6f6586bb1 | train | human | |
a_{n}\notin O(2-\epsilon)^{n} | 2dc588dc900bdb87 | train | human | |
\bigcap_{i\in I}A_{i}<\infty | 4d2e8f592294baed | train | human | |
\int cos^{2}xdx | 5bf3447ce052e8ba | train | human | |
\tilde{f}(s)=\frac{a_{N}}{s-N}+\cdot\cdot\cdot | 2c9e329c40ee25f5 | train | human | |
\frac{P(s_{1})}{P(s_{2})}=\frac{\Omega_{R}(s_{1})}{\Omega_{R}(s_{2})} | c95f860dc81ccd1a | train | human | |
U=\int f(v)E(v)dv | b92e7f9596e1322a | train | human | |
(\begin{matrix}0&1\\ -1&0\\ \end{matrix}) | 62bc017ba640ea79 | train | human | |
[\begin{matrix}1\\ 0\end{matrix}] | 6ad871c4a069fb52 | train | human | |
V_{2}P_{2}-V_{1}P_{1} | 1642092128574636 | train | human | |
(\begin{matrix}p\\ n\end{matrix}) | f3133836ec0ab3dc | train | human | |
P(k,k^{\prime})=\frac{E_{kk^{\prime}}}{\langle k\rangle N} | b073d8b6843508a5 | train | human | |
||x+y||^{2} | da55c00479c2cd03 | train | human | |
T_{0}=T+\frac{V^{2}}{2C_{p}} | 245a9799c753c2bb | train | human | |
273^{4}+26+403 | 0d6e5c48f3a9fb4e | train | human | |
j(\tau)=\frac{(x+16)^{3}}{x} | e020e6affbe50f86 | train | human | |
\tilde{\gamma} | 9c16c20b90e85aa2 | train | human | |
\frac{2^{x}}{x!}<\frac{C}{2^{x}} | 46384a3b5facb4d7 | train | human | |
{{11^{9}}^{9}}^{\frac{6^{7}}{151}} | d6986145fe0bf08a | train | human | |
a_{1},a_{2}\in A_{\ge0} | f31b0119622377e0 | train | human | |
\hat{V}_{n} | cb8c5b8286495df0 | train | human | |
\frac{d^{3}}{dx^{3}}G(x)\ge0 | cc93e53b2e137623 | train | human | |
(f_{1})_{a}=\frac{1-r_{2}}{2-r_{1}-r_{2}} | 4403c544e28758f2 | train | human | |
\int_{0}^{T}f(t)dt | 84b2355abb63de53 | train | human | |
(\begin{matrix}bi&z\\ -z&di\end{matrix}) | 0d3edabcb003fa91 | train | human | |
\tilde{f}(x) | 12623448bde3ab24 | train | human | |
\tilde{n}=n+z^{2} | e3ce24cd7665b2a4 | train | human | |
\tilde{E}_{6} | 5d0a548955d095a5 | train | human | |
|\frac{\partial S}{\partial y}|\ll1 | 9670281708bab45b | train | human | |
e^{2}=\frac{1}{2} | f846307dc55eb15b | train | human | |
\epsilon_{2}=\lambda^{\lambda^{\lambda^{\cdot^{\cdot^{\cdot}}}}} | a8ee67c9f97f2e29 | train | human | |
K\in N^{+} | 1bd106de869d15b4 | train | human | |
\gamma_{i}\equiv\frac{1}{\sqrt{1-\frac{e_{i}+e_{i}}{o^{0}}}} | 3d1f7aca03ac1c14 | train | human | |
\hat{H}(t) | 5e6ab461adf409c5 | train | human | |
|2\rangle=(\begin{matrix}0\\ 1\end{matrix}) | c699bdca9f4fd0e1 | train | human | |
\tilde{f}_{0}() | ea4b31f724e07c29 | train | human | |
f(x)=x^{-\alpha} | c9beea35a8228b19 | train | human | |
|U_{e3}|^{2}=0 | b259f3086e6a1c9a | train | human | |
y=\sqrt{\frac{sec^{2}u}{tan^{2}u}} | 7c72adcc162eefe8 | train | human | |
\pm\hbar=\pm\frac{h}{2\pi} | 0d4e91e4cb21fb12 | train | human | |
\frac{(5-5)^{7}}{7\cdot7} | 7b93d5a3a673fa43 | train | human | |
[\begin{matrix}-1&1\\ 0&0\end{matrix}] | 53933cca67b09e7d | train | human | |
(y^{\mu})^{-}(y_{\mu})=0 | e3e1a050ac64df21 | train | human | |
\sqrt{19} | 220edf76f56ab219 | train | human | |
\frac{p^{2}}{a^{2}}+\frac{z^{2}}{b^{2}}=1 | 6d001a4ec2581295 | train | human | |
\alpha=1/\sqrt{\beta_{c}} | 0a26e406810191e3 | train | human |
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