image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1 value | data_type stringclasses 1 value |
|---|---|---|---|---|
\beta=\frac{1}{3}(2e^{i\theta}+e^{-2i\theta}) | ce716e89e8fa7cce | train | human | |
a\cdot\frac{m}{s}:=\frac{am}{s} | 71226a9b93c37268 | train | human | |
\frac{8}{9}\sqrt[4]{2} | 7bd354ce20392ba4 | train | human | |
(\begin{matrix}n\\ 2\end{matrix}) | afd3678a3bffeda6 | train | human | |
(\frac{\sqrt{150}}{6})^{(5-188+9)} | 02d29ce7cf22d942 | train | human | |
c(\nu) | 32bb4392d52609a3 | train | human | |
k_{1}^{k_{2}^{k_{6}^{-^{-^{-}}}}} | 5e58233d77f430d5 | train | human | |
H_{(1-X)}=\frac{\beta-1}{2\beta-1} | 0a36f9edf84c7b70 | train | human | |
d(C_{n})=\lceil n/2\rceil | f05236a4046068df | train | human | |
y=\frac{y_{A}}{\sqrt{4-\frac{4}{c^{2}}y_{A}^{2}}} | b0395607d99861db | train | human | |
184+414+408^{163} | 623949c18156f4d2 | train | human | |
(A\backslash B)^{c}=A^{c}\cup B | 988aa4fdbd0219a4 | train | human | |
e^{38^{38^{38^{322}}}} | cd0e815115a4efe4 | train | human | |
\epsilon>0 | fbf1a6a36cdc0c7f | train | human | |
\frac{8\pi g}{\sqrt{9-\frac{2g}{rh^{2}}}} | d2de37cbe585f598 | train | human | |
\frac{X}{Y}\sim Pareto(1,n) | 506c993f572c30a8 | train | human | |
\frac{c^{2}}{2}<a^{2}+b^{2}<c^{2} | 9e744b75146bef2e | train | human | |
a^{a^{-^{-^{a^{a}}}}} | 1a5ac52ff4a8c971 | train | human | |
\frac{LE-25}{85-25} | 41333d5a14736ffb | train | human | |
\epsilon:X^{*}\otimes X\rightarrow I | c33ea2b647cc710d | train | human | |
E_{i}=cF_{0i} | 6387fd7fc11f143e | train | human | |
\int_{D}f\Delta g=0 | f3bfd24039d04500 | train | human | |
\tilde{B}_{8} | 4c718d5be3a65861 | train | human | |
\int f(x)dx=F(x) | 887920383e8e25cb | train | human | |
\tau=\frac{T}{T_{c}} | baf0eb28d2e157ef | train | human | |
E^{\prime\prime}=\frac{1}{y^{\prime\prime}}+\frac{y^{\prime\prime2}}{2} | 20a5fde415882eef | train | human | |
(\begin{matrix}0&0\\ 0&e\end{matrix}) | 2337b5aa28a74636 | train | human | |
t,(t<s) | e8e1e2d6c8249b36 | train | human | |
\omega_{c}=\frac{0}{\sqrt{V_{\frac{0}{2}}J_{\frac{0}{2}}}} | 01a637d2b59fa245 | train | human | |
C_{0..n} | 929f681f2f3debe2 | train | human | |
1/\sqrt{2} | d9ca692beb8bf68b | train | human | |
M=[\frac{1+\frac{C}{D}}{\frac{C}{D}+\frac{R}{D}}]B | 2e7cf15ede0f59fe | train | human | |
c=\frac{\partial C}{\partial m} | 124b2eb6c463b98e | train | human | |
{193^{8}}^{2-199} | dd046a430c148349 | train | human | |
\hat{V}_{n} | 5f433f844432dbde | train | human | |
\overline{\overline{x}}^{i}=B\overline{x}^{i} | 08bf9db43385b731 | train | human | |
s\notin\alpha,t\in\gamma | 05a4375f44a8a37d | train | human | |
\overline{K} | e23bd6c72af5bf36 | train | human | |
E=\frac{N_{1}\cdot N_{2}}{d} | ae0fa146ba04ff35 | train | human | |
M^{-1} | 6099cb0f92ee3564 | train | human | |
d\tilde{V} | d09a4f582ef9cef9 | train | human | |
(\begin{matrix}a&z\\ \overline{z}&c\end{matrix}) | 8b2f6693d88e3905 | train | human | |
1+G(s) | 02d12211f7f2f897 | train | human | |
r_{+}^{2}=M^{2}+Q^{2} | f8d4bbe100bec3b7 | train | human | |
\hat{m}_{+} | 0f97bf07ccf71c42 | train | human | |
y(1)=1 | 0582c8c2af216822 | train | human | |
H^{\infty}(C_{+};L(X)) | 683255a5fdc0fb6e | train | human | |
\delta\in(0,1/2) | 1d109583ebe2f1c3 | train | human | |
\sqrt{G_{i}}=\sqrt{\sum_{\tau=1}^{t}g_{\tau}^{2}} | 6cbb21dc3fab4906 | train | human | |
\theta_{k}^{b} | f50abac0d06be302 | train | human | |
((\frac{5}{17})^{1})^{(270^{2}-8)} | 693bfb8ed01b179d | train | human | |
\{\} | 084f8f19f7fef1b5 | train | human | |
-\int_{P_{1}}^{P_{2}}VdP | c48e8b1d9281b8ba | train | human | |
sec\varphi=\frac{1+t^{2}}{1-t^{2}} | 679c46e2378f2d33 | train | human | |
+-+ | b4f27368c478a26b | train | human | |
\int\frac{dx}{lnx} | 99a35e9537267571 | train | human | |
\alpha_{avg.} | 3a45bb9a428730bd | train | human | |
it=ln(\frac{iy+F}{iP+F}) | 3c9ffea73b98d011 | train | human | |
v=\frac{\overline{X}_{8}-\overline{X}_{2}}{\sqrt{\frac{h_{8}^{2}}{N_{8}}\cdot\frac{h_{2}^{2}}{N_{2}}}} | a0c06befade238a8 | train | human | |
\frac{\partial\rho}{\partial t}=0 | df770c6bccda3d33 | train | human | |
n^{\overline{m}} | e8e88a622885e6e3 | train | human | |
x^{\underline{n}}=x(x-1)\cdot\cdot\cdot(x-n+1) | d4777decbc802210 | train | human | |
N_{i}=(\begin{matrix}8\\ i\end{matrix})i^{12} | 0f62ffaff96d8b90 | train | human | |
\{\begin{matrix}x&y\\ z&v\end{matrix}\} | e543aab93b77763b | train | human | |
\frac{40}{3}\times\frac{3\times67}{16} | 8d98957444a5c4b0 | train | human | |
i_{RMS}=\sqrt{2eI\Delta f} | 133b269567665851 | train | human | |
(\{a_{ij}\},k) | eb6acf9829ec180c | train | human | |
[\begin{matrix}a&c\\ 0&b\end{matrix}] | d164b285288fe2e4 | train | human | |
y^{y^{-^{-^{y^{x}}}}} | c65bfa719fdc3524 | train | human | |
\frac{\frac{7}{1}}{(2/352)} | 9fa7d8cc0d755f3a | train | human | |
\int sin(cos(x))dx | 23c893dd6bf19381 | train | human | |
(\pi(g,\gamma)1,1)=\gamma^{-1}. | d9d78ca9c9fcceb0 | train | human | |
\frac{1}{2}\pi R^{2}D | 0b932c23f0bdb3ac | train | human | |
\frac{d^{3}}{dx^{3}}[x^{4}]=24x | 96f41588b87bae5e | train | human | |
[-P^{T}|I_{n-k}] | a21fbefbb3bc5a18 | train | human | |
\frac{1}{1-\lambda t} | f6f736bab84a95f8 | train | human | |
\hat{y}\in\{-1,1\} | 1107d81793d2da04 | train | human | |
s=O(n/\epsilon^{2}) | fbed91d0cb03da44 | train | human | |
G^{\prime}=\frac{\sigma_{0}}{\epsilon_{0}}cos\delta | cc80fa2a760e0305 | train | human | |
(4+8+7\cdot{1^{100}}^{\sqrt{7}}) | 8ffee67bd5e77245 | train | human | |
(\frac{374}{2}/406)^{7^{2}\cdot2} | c791e78c07275c79 | train | human | |
\frac{\frac{237}{445}-431}{\frac{10}{164}} | cbe30fdd8468e847 | train | human | |
u=tan\frac{x}{2} | bb73c811148e1d33 | train | human | |
v=\sqrt{\frac{2E}{m}} | eb0340375323fe0c | train | human | |
\prod x_{i} | 0da1ac2c404281c3 | train | human | |
\frac{dT}{T} | c79049c4cc6146fa | train | human | |
\frac{\frac{10}{7}}{\frac{\sqrt{450}}{2}} | 40b605f7009d805e | train | human | |
\int_{0}^{1}f^{\prime}(x+th)dt | 39eb2640511d41af | train | human | |
e^{-i\varphi}=\frac{1-it}{1+it} | d127b27ce5742afc | train | human | |
(f_{1}(x))^{s_{1}}(f_{2}(x))^{s_{2}} | 41f5a8385e770e5f | train | human | |
-2\int Edl | 1c75df8887c89e79 | train | human | |
W(1-(1-\beta)F_{t}) | 5cbccf0600d873cd | train | human | |
v=\sum_{i}v^{i}\frac{\partial}{\partial x^{i}} | 7af549be482c8043 | train | human | |
\frac{\partial V}{\partial R} | e0104fefb92ee56b | train | human | |
(97/108)-22^{\frac{75^{3}}{5}} | f1cfee8dcbc01f32 | train | human | |
[\begin{matrix}0&1\\ 0&0\end{matrix}] | 594cd7e996c32ea4 | train | human | |
t_{0.975,n-1}\simeq2 | 4cbf0f9c6b7b403e | train | human | |
P_{3}=(0,-72,2\sqrt{3},12) | 604b88ff8ccb853b | train | human | |
\frac{\partial T}{\partial t}=\kappa\frac{\partial^{2}T}{\partial^{2}z} | a4f4657cc3c87d92 | train | human | |
I_{1}^{m} | a077ef8053d4feb2 | train | human |
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