image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1
value | data_type stringclasses 1
value |
|---|---|---|---|---|
k | 6fa518517fc0a7fc | train | human | |
\tau_{true}=\frac{d_{spacing}}{c} | d894943a83e89dcc | train | human | |
2^{7/12}=\sqrt[12]{128} | 4e57c7fc95d1cf1a | train | human | |
\gamma(n)=\prod_{p|n}p | 4e7de2e9fff4bd20 | train | human | |
\frac{\partial^{2}z}{\partial t^{2}} | b3a80747fdaacdce | train | human | |
\Delta^{\prime}-\Delta=-\frac{1}{4}Sc | 6361abdcabd2a4ca | train | human | |
(\begin{matrix}13\\ 10\end{matrix})=(\begin{matrix}13\\ 3\end{matrix})=286 | 3f9e2ec95bea76c1 | train | human | |
(\frac{(164-242)}{\sqrt{5}})^{\frac{283}{9}} | 0c73f2ecb9a358a0 | train | human | |
2(\begin{matrix}n\\ j\end{matrix}) | 25a9ed5a7bfafe87 | train | human | |
\hat{n} | 47ed8fd52e6294c9 | train | human | |
\hat{J}_{z} | c4c19b88de81a9d2 | train | human | |
(\frac{271^{4}}{101})^{(\frac{68}{301})^{123}} | 70677362b10c5d66 | train | human | |
(\frac{9!}{8!\cdot(9!-8!)})^{9!} | 6c71966c8cc2b532 | train | human | |
m_{e}\approx\frac{1}{3}m_{d} | b82a2321bba02430 | train | human | |
\int_{0}^{t}p^{\prime}(s)p(t-s)ds | 4145a219f437abe6 | train | human | |
\nabla=(\frac{\partial}{\partial x},\frac{\partial}{\partial y},\frac{\partial}{\partial z}) | a8ebbb110aaf716f | train | human | |
M=(\begin{matrix}A&B\\ C&D\end{matrix}) | 5a46dfcd6c76bc6d | train | human | |
\overline{A}=\frac{\sum_{g=1}^{G}A_{g}}{G} | 9417424fba50268f | train | human | |
(\begin{matrix}n+1\\ k\end{matrix}) | 72cfb64ae3ddfbdc | train | human | |
\sqrt{2}=1 | 2feccd0a0d7ae98e | train | human | |
B_{\tilde{\nu}} | 2be8aafa9ac96ab5 | train | human | |
N\approx\frac{f^{2}}{c}\frac{D_{F}-D_{N}}{2D_{N}D_{F}} | 0e16313e756a376b | train | human | |
S\subset\{1,\cdot\cdot\cdot,N\} | 61fda759d606dfc1 | train | human | |
7^{7^{\cdot^{\cdot^{\cdot^{j}}}}} | d07faf12b38b1ec6 | train | human | |
\frac{e^{\cdot\frac{9}{x^{5}}}}{x} | 0fbc84ca7e9c8c38 | train | human | |
\frac{d}{2} | a865433629f4fac1 | train | human | |
g^{t}(x):=tg(tx) | 8189811b1823fece | train | human | |
A_{\mu}=\eta_{\mu\nu}A^{\nu} | ef86c7f4fcfa84fc | train | human | |
I=\frac{1}{3}ml^{2} | 6d4e2886967ad940 | train | human | |
[\begin{matrix}0&0\\ 1&1\end{matrix}]:b | 0b74e879e6237ed2 | train | human | |
\int cos(\lambda x)dx | ea4dc4fd8fc2faea | train | human | |
f(z)=1/g(z)+c | a84ef45f6a81d1b1 | train | human | |
\theta\vdash_{\vec{s}}\phi | c5bc9786ddb8f959 | train | human | |
\mu_{n}=\lambda_{n}^{2} | 49e0019e9e7bf585 | train | human | |
z=\frac{h}{\sqrt[8]{\cdot\frac{u_{1}}{5}}} | 3615d330f99a1784 | train | human | |
\int2xdx=x^{2}+C | af1d61f0f3e23165 | train | human | |
\lambda_{th}=\frac{h}{\sqrt{2mE_{K}}} | 3b3106725c6456ee | train | human | |
-(\frac{\sqrt{5}+\sqrt{7}}{2}) | 3230a3d7502241db | train | human | |
P_{s}=\frac{P_{c}\cdot4\cdot l}{m\cdot l_{m}} | eb9c4cf1c83f6454 | train | human | |
\int_{-3}^{4}f(x)dx | e5cbcee46db744d1 | train | human | |
\zeta=-\beta tan\frac{\pi\alpha}{2} | 432b1b81db707625 | train | human | |
Q=\sqrt{\frac{{H_{0}}^{7}J_{1}}{H_{7}H_{4}J_{7}}} | eb51cec2baa1dd88 | train | human | |
(\begin{matrix}n\\ 3\end{matrix})-\lfloor\frac{n}{2}X\rfloor | 8f4b8d90c65c39f8 | train | human | |
\pi_{w}^{\eta} | aa49fbcc3ac519d7 | train | human | |
\frac{|ax(t)+by(t)+c|}{\sqrt{a^{2}+b^{2}}} | 7861292cd59e8086 | train | human | |
O(|E|+|V|\sqrt{log|C|}) | a33efe0de3ee9471 | train | human | |
\Psi^{\dagger}\gamma_{0}\gamma_{\mu}\Psi | bb245acb7222faa0 | train | human | |
\frac{\partial N}{\partial R} | b79ebf6b37f52b06 | train | human | |
\sqrt{\frac{10}{63}} | 9af5bfe8f51b63a1 | train | human | |
d(1/z)=-\frac{1}{z^{2}}dz | 031afc9a89835268 | train | human | |
\gamma(n)=\prod_{p|n}p | 21450f71ee169f23 | train | human | |
\frac{n+\sqrt{n^{2}+4}}{2} | 1ca6d3f3fc9c148a | train | human | |
1-1\sqrt{2}=-0.41421... | 52349fe01cc28393 | train | human | |
S=\int wdx | baff36f56021c672 | train | human | |
Z=(\begin{matrix}z&0\\ w&-z\end{matrix}) | b103871a954d3537 | train | human | |
\kappa^{-1}=\frac{1}{\sqrt{8\pi\lambda_{B}N_{A}I}} | 6fd3462998f5ce82 | train | human | |
1=(\begin{matrix}1&0\\ 0&1\end{matrix}) | 33f819001c3e52d3 | train | human | |
P_{ij}^{-1}=\frac{\delta_{ij}}{A_{ij}} | d7bdee564f82aaec | train | human | |
\sum_{i=1}^{N}a_{i}x_{i}=-a_{0} | 84e3addc5775ec50 | train | human | |
|i-k|+|j-l| | 2c15f7643c32f39f | train | human | |
u_{i}=\frac{x_{i}}{n_{i}} | 47b88a4fc2ffff02 | train | human | |
y(\underline{n}) | 885793aa3d6bd633 | train | human | |
v=\frac{\partial g}{\partial y} | 068d1645be46105a | train | human | |
(\begin{matrix}n+k-1\\ n-1\end{matrix}) | cd3fa39a8f1047ba | train | human | |
\frac{d^{2}}{dx^{n}} | 75f5ac2d5b9274f3 | train | human | |
\frac{1\cdot\frac{j}{c}cos\epsilon_{s}}{\sqrt{1-\frac{j^{2}}{c^{2}}}} | 933ee0373d267019 | train | human | |
\frac{8^{485}}{4}-257\cdot6 | 4b2917883182022a | train | human | |
\sqrt{\frac{BA}{k*n}} | 2709abe283ac2bdc | train | human | |
y^{*}=\frac{y}{L_{c}} | c438b63f7835e5db | train | human | |
\frac{3+\sqrt{21}}{2} | afd30f58c9905802 | train | human | |
3\cdot10^{{6^{1}}^{1}} | 9dff8be5037c4c3e | train | human | |
z_{p}=\frac{bf}{d} | 1f985541ef11b59a | train | human | |
T(z)=T_{0}e^{\frac{\alpha}{2}z} | 0b7ccf8702b2869d | train | human | |
\Phi=\frac{1}{\sqrt{1-\frac{s^{2}}{i^{2}}}} | 6cc4ccca1325bff8 | train | human | |
\varphi_{\delta}^{6} | 02b68514ef3d2e32 | train | human | |
\delta(n_{1},n_{2},...,n_{m}) | 13d65c3c84991645 | train | human | |
\tilde{D}_{9} | adde26f6805265fb | train | human | |
\sum_{k=0}^{m}(\begin{matrix}m\\ k\end{matrix})(\begin{matrix}n\\ r+k\end{matrix}) | 1d46e1f6f7720f0f | train | human | |
\hat{O}^{\prime} | 58a4790b018ff1d6 | train | human | |
\frac{{8^{\sqrt{43}}}^{382}}{(\frac{215}{430})^{72}} | 446a8518859cf0dd | train | human | |
\prod_{i}X_{i} | 72bb36726b7da0a1 | train | human | |
\varphi=2\cdot D_{1/2}(h*\varphi) | fa972a16fcaf8a66 | train | human | |
\pi:G\longrightarrow B(H) | ffa8867353f2dc81 | train | human | |
\underline{P}(Cl_{t}^{\ge}) | 8fa293fa4eabfd88 | train | human | |
S=\sqrt{L^{2}+(x+a/2)^{2}} | afb55c60401a3a0e | train | human | |
tan(\alpha/2)=\frac{d/2}{S_{2}} | d865c5cff5d9b512 | train | human | |
9\cdot5^{\frac{\frac{7}{399}}{324}} | dd261ebc9898e8af | train | human | |
\zeta(n)>2^{n/2} | 73a5da20431ff732 | train | human | |
A\underline{\delta}_{\Phi}B | e985ef017642d878 | train | human | |
[\begin{matrix}s&t\\ u&v\end{matrix}] | 01ad7ed949aa15df | train | human | |
L^{\infty}(X,U,\mu) | e31e42451e0c4b53 | train | human | |
R=F^{2} | 69cfc291db282979 | train | human | |
F(t)=\frac{t^{3}}{3} | 7b6fdba63114b20e | train | human | |
\frac{{\sqrt{1}^{8}}^{10}}{468^{372}} | 46a51624dd5ff1b2 | train | human | |
\frac{\partial\omega}{\partial k} | fa71aaec5492f64b | train | human | |
(\begin{matrix}0&1\\ -1&0\end{matrix}) | 6e43e7d43dceb31b | train | human | |
(1-\frac{r_{s}}{r})\frac{dt}{d\tau}=\frac{a}{b} | c50ddf9d79270cc4 | train | human | |
\int_{0}^{T}g(t)dt | 807fec911b6ea398 | train | human | |
Gal(F_{p}^{\infty}(K)/K) | a4dd68406c04eb6c | train | human | |
\hat{n}_{b} | 855e5e20144d07ae | train | human |
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