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}-\frac{1}{6}\sqrt{3} | a38d80b24435a9f5 | train | human | |
sech(z)=\frac{1}{cosh(z)} | a89e9cc95a7d669e | train | human | |
M=\frac{\pi abc\rho}{6} | c95d86ba46c372b3 | train | human | |
\frac{\partial\eta}{\partial y}>0 | 961bff6a2f7e299c | train | human | |
F=\frac{q_{1}q_{2}}{r^{2}} | a2a50b9bfc5da22e | train | human | |
\frac{(7\cdot3)^{301}}{{10^{6}}^{3}} | aeb907786e193ac5 | train | human | |
\frac{f^{(k)}(\xi)}{k!}x^{k} | b83dab6bfc3c52a1 | train | human | |
(\begin{matrix}n\\ n\end{matrix}) | 75f2d5d3277df531 | train | human | |
w(n)\le\lfloor(n-1)/2\rfloor | 90f1146c0f0a2bd0 | train | human | |
\int_{0}^{T}PdX=nh | 31b73489a4c6b25f | train | human | |
r(K_{m}+\overline{K_{n}},K_{p}+\overline{K_{q}}) | afba50900610ca23 | train | human | |
[\begin{matrix}1&0\\ -G&1\end{matrix}] | fe0fbcb08f9de034 | train | human | |
(\begin{matrix}0&-1\\ 1&0\end{matrix}) | 8839732b155f17d8 | train | human | |
053^{053^{053^{053^{057}}}} | d659646548752044 | train | human | |
\eta_{th}=1-\frac{1}{r^{\gamma-1}} | f0ab3e93f0d4750e | train | human | |
x^{13^{13^{13^{122}}}} | 3bd1705b92231714 | train | human | |
A,B,E\in2^{X} | c38c1b919dbbbf02 | train | human | |
v(r)=(rd\Phi/dr)^{1/2} | 562680bcba49961b | train | human | |
X_{j}=\frac{\partial g}{\partial\xi_{j}}|_{\xi_{j}=0} | 48cc0b821dd014b2 | train | human | |
c_{k}=0 | fe360fcd6e53953c | train | human | |
2\sqrt{2} | 2489a8720c855f15 | train | human | |
T_{b}=\frac{I_{\nu}c^{2}}{2k\nu^{2}} | 4a4cb45bbd306585 | train | human | |
(2e^{0i})^{0.5}=\sqrt{2} | c429f115a7c8b8da | train | human | |
(\begin{matrix}n-1\\ i\end{matrix}) | 8c582a2a1c708970 | train | human | |
(\begin{matrix}N\\ M\end{matrix}) | 3df97c2a7cdf48fb | train | human | |
\rho=\frac{1}{2}r(1-r) | a22d7bf3057af579 | train | human | |
\frac{\partial\delta}{\partial x_{j}}(x) | 3c62d4f99f0e0e2b | train | human | |
{281^{203}}^{52-1} | f387eca3bf67001e | train | human | |
b_{n}=\sum_{d|n}\mu(\frac{n}{d})a_{d} | 7a93a23f13e42b8d | train | human | |
lim_{x\rightarrow0}\frac{1-cosx}{x^{2}}=\frac{1}{2} | 660c60436117ac56 | train | human | |
(\begin{matrix}0&1\\ 1&0\end{matrix}) | d15e7ac49bb56d08 | train | human | |
D_{\mu}=\partial_{\mu}-i\frac{e}{\hbar}A_{\mu} | 54e2624734844c67 | train | human | |
\underline{S}_{\lambda} | f65211e5d923b122 | train | human | |
P_{t}=\frac{x_{t}+x_{t-1}}{2} | 44fcff412a78862c | train | human | |
G_{1}\in[0,255] | b4715a0cc9c30219 | train | human | |
\frac{dp_{o}}{p_{o}} | 8a424198bda424d3 | train | human | |
\frac{4}{\sqrt{4-\frac{v^{9}}{x^{9}}}} | bbfc517660a54700 | train | human | |
I_{2}=-\frac{Z_{21}}{Z_{22}}I_{1} | 68f6c9f5685f4b54 | train | human | |
\psi,\tilde{\psi} | 6791cf9d01d8a754 | train | human | |
\frac{\sqrt{3}\cdot\sqrt{168}}{(\frac{413}{3}\cdot326)} | 170313490fc019c5 | train | human | |
(i\omega_{1},i\omega_{2}) | b8c4f18be1846949 | train | human | |
t=\frac{2L/c}{\sqrt{1-v^{2}/c^{2}}} | 9f7c9fef5751e45b | train | human | |
D^{(r)}X^{n}=(\begin{matrix}n\\ r\end{matrix})X^{n-r} | 5550bb54ce1fecbe | train | human | |
\frac{dW}{dt} | 16d83b4e97de58a1 | train | human | |
\tilde{f}_{0}:X\rightarrow E | 4595dbf157498a5a | train | human | |
2\sqrt{n} | 7d8dc0458df1ea6b | train | human | |
\int_{-a}^{a}f(x)dx=0 | a73779ad8ee1b1e9 | train | human | |
e^{\cdot\frac{(F\cdot M)^{0}}{0{(s_{F})}^{0}}} | baffe7beb70243b2 | train | human | |
2^{2^{2^{2^{74}}}} | bb688f22742e99b6 | train | human | |
Q_{4} | e9c15afd4d4c0046 | train | human | |
E=\frac{mg^{2}}{\sqrt{5\cdot\frac{w^{2}}{g^{2}}}} | b4ceb27e5e94d9bf | train | human | |
(\begin{matrix}n\\ p\end{matrix}) | cd2e982cb0f7d65a | train | human | |
b(m)=e^{m/T} | 13291c72394e9fcf | train | human | |
\prod_{i}S_{i} | 4ddf5b38b19fa210 | train | human | |
\int(p(x))^{n}f(x)dx | de21a16122121304 | train | human | |
\underline{v_{row}}=2 | 24cf5532e3ac76e1 | train | human | |
|f^{\prime}(0)|=1 | 7e113da49b5bba7d | train | human | |
\{R_{t}\}_{t\in D} | 927bd8f4bfa893b0 | train | human | |
(S^{3})= | 0412f13ec9bf1cb7 | train | human | |
\beta_{T}=\beta_{S}+\frac{TV\alpha^{2}}{Nc_{P}} | 064da36670efeb8f | train | human | |
\prod_{i=1}^{n} | 0efb07e3b2c94ea4 | train | human | |
d_{1}=[\begin{matrix}x&y\\ \end{matrix}] | aaaa548e13d78cd8 | train | human | |
F_{m}\approx-\frac{\mu_{0}I_{1}I_{2}}{2\pi r} | 0745dc1e393efa87 | train | human | |
T_{0}\approx2\sqrt{l} | b584509d8fc32e45 | train | human | |
\tilde{O}(\theta dlog\frac{1}{d}) | c79c7c99af5c649a | train | human | |
\underline{V} | 2cac26fb519729ae | train | human | |
\int dx=0 | b9d356d7eb47c35c | train | human | |
\Rightarrow v=\sqrt{2gz} | 5153a20b92ef77c0 | train | human | |
j\notin T | 6aeebd8a4137e779 | train | human | |
M=K[\begin{matrix}R&t\end{matrix}] | 557fd1f762cbbded | train | human | |
\forall X,Y\in L^{0}(F_{T}) | fc9d0a3b44e50668 | train | human | |
(\frac{10}{164}+7)^{\frac{10}{451}-\sqrt{21}} | 0b3423cf1f05f32d | train | human | |
[\begin{matrix}4&6\end{matrix}] | 7767eab105eb8735 | train | human | |
M=\int_{V}\rho dV | 20449b7b725d2113 | train | human | |
(\frac{3/345}{130})^{2^{3}/4} | 5d24932c6ebf5b7b | train | human | |
a_{n}=e^{i\frac{2\pi}{q}x_{n}} | 7aa4be8ad29d5f9e | train | human | |
n_{0}=\frac{p_{0}N_{A}}{RT_{0}} | 4a7b83c9a7d3c70c | train | human | |
\overline{abc} | 91a773c4242b390e | train | human | |
tan\gamma=\frac{d}{R} | 637b6b275680ffd4 | train | human | |
(\begin{matrix}6\\ 4\end{matrix}) | 7927b0b546602095 | train | human | |
p\notin F(t)(\partial\Omega) | 290b51283c5f8ec4 | train | human | |
\frac{\partial g}{\partial x} | cb56a626f4ef1fb7 | train | human | |
\Delta s^{\prime}=\frac{\Delta s}{\sqrt{1+\frac{v^{5}}{u^{5}}}} | c6da24b83abf477b | train | human | |
\tilde{A}_{7} | 4628c6115b00544f | train | human | |
V=\frac{\sqrt{2}}{6}a^{3} | a737824b73d67423 | train | human | |
\frac{p}{q}=\frac{a+c}{b+d} | ba9ca81ae7732191 | train | human | |
9\cdot5^{\frac{\frac{7}{399}}{324}} | ec67f861c0b9bc29 | train | human | |
T(3,1)_{-\frac{1}{3}} | 2af42881870fca41 | train | human | |
cosx=\frac{e^{ix}+e^{-ix}}{2} | a496cc813b710e1c | train | human | |
a^{s^{n^{\cdot^{\cdot^{\cdot}}}}} | 4ad9dd3587887062 | train | human | |
Q^{(ab...n)} | 6ca41256db3ce39b | train | human | |
f(z)=\sum_{k=0}^{\infty}(\begin{matrix}1/2\\ k\end{matrix})z^{k} | be5c6f7aa296abb6 | train | human | |
\int x^{s}\phi(x)dx | c9f34b6f82fce077 | train | human | |
2\sqrt{n} | 2e4985970b125e17 | train | human | |
\hat{s}=S(S+N)^{-1}d | 7d7c39f55a4b2b96 | train | human | |
\frac{\Gamma_{s}A_{s}}{{\delta x}_{SP}} | a1abfc39d924adb7 | train | human | |
[\begin{matrix}p&t\\ q&u\end{matrix}] | b4b9ac8f63079774 | train | human | |
(\begin{matrix}n\\ b\end{matrix}) | f0eff8d2bd111762 | train | human | |
\hat{v}_{k} | 3e2f23ef854ee620 | train | human | |
n=\frac{m_{9}v}{\sqrt{1+\frac{v^{3}}{c^{3}}}} | a1b5bc906b2034f4 | train | human |
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