image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1 value | data_type stringclasses 1 value |
|---|---|---|---|---|
\eta_{0}(e^{-\Phi}Q_{B}e^{\Phi})=0 | 8438e043e404b0a8 | train | human | |
\frac{m}{\sqrt{\frac{e^{2}}{n^{2}}-1}} | 94eaf83b28e0e0cf | train | human | |
F(x)=\underline{\int_{a}^{x}}f(t)dt | dc9d524d94a866f9 | train | human | |
\tilde{M}=M//G | 834a1a6b1a65d946 | train | human | |
E=\int Fudt | e6dceac562560954 | train | human | |
\int_{1}^{5}2xdx | fbd2f144aa14d07b | train | human | |
C=-\sqrt{2}+\sqrt{3} | 6efb89b317c96e0b | train | human | |
s\notin\alpha,t\in\gamma | 29476ec4d1a16e7b | train | human | |
\frac{f_{r}}{f_{y}}=\frac{1}{\sqrt{1-\frac{i^{5}}{a^{5}}}} | d17f5b403d816f71 | train | human | |
[A]_{ij}=a_{i}\cdot a_{j} | 7dcd5116c8022b16 | train | human | |
\sigma=\hat{f}(\epsilon) | c65299d7f7ac80fe | train | human | |
G(t)=\int_{0}^{t}g(s)ds | 97b2974853db422b | train | human | |
\overline{s}\in\alpha,t\notin\gamma | 2162febad2c4d250 | train | human | |
M=\int_{V}\rho dV | 88b321521f6016f2 | train | human | |
\int_{0}^{x}1dt=x | 502d0680254b2e16 | train | human | |
\lambda=\lambda_{0}\sqrt{\frac{c-v}{c+v}} | f81ab06957973960 | train | human | |
vol(\Omega^{*})=vol(\Omega) | 9fee0cb7a0b35ff1 | train | human | |
K=s^{s^{s^{...^{s^{f}}}}} | e234f7dc4661b2b1 | train | human | |
\hat{\rho} | 85e25d53ed304b37 | train | human | |
R_{ab}=\frac{2\Lambda}{n-2}g_{ab} | 4420cf5ca61f3208 | train | human | |
\delta=\frac{P}{P_{0}} | cd30f24cc5490238 | train | human | |
(\frac{\frac{45}{4}}{101})^{320^{125}} | 6f21c3041c6f67b5 | train | human | |
M=\int_{V}\rho dV | 1fdd28df33289ec8 | train | human | |
t_{0}=\frac{1}{\sqrt{3}} | 7849d66e9e7756b9 | train | human | |
\sqrt{\frac{16}{35}} | 00e17a5de2fcdd91 | train | human | |
r=1.224\cdot w(z) | e4a8ef0bf739bb1a | train | human | |
\frac{484^{6}-287}{(\frac{10}{\sqrt{3}})^{\sqrt{151}}} | d0b7404776e08e36 | train | human | |
R=S(\frac{Et^{2}}{\rho})^{\frac{1}{5}} | 995fb0ff29a46fe7 | train | human | |
(\begin{matrix}6\\ 5\end{matrix}) | 9432f1b474bd65b6 | train | human | |
F[x,y]=\int_{E}xydt | d7c4d70d7689d770 | train | human | |
f^{i^{c^{\cdot^{\cdot^{\cdot}}}}} | 50023810e4fe444b | train | human | |
\Delta=\frac{\partial\rho}{\rho} | 16b2a1411415eef9 | train | human | |
\tilde{b}_{ij} | 805e144a87346569 | train | human | |
\frac{1}{\sqrt{4\pi}}D | f44dcff07844a26b | train | human | |
\sum_{n=1}^{\infty}f(n)^{2}<\infty | f24996549075dbb5 | train | human | |
\hat{D} | 05b754eb20a656ce | train | human | |
\sum_{i=0}^{\infty}n_{i}=dN(\nu) | 007585af6cd70e41 | train | human | |
\frac{1}{f(x)}\cdot f^{\prime}(x)=1 | b4e636028d7b8089 | train | human | |
s=r\dot{\theta}=\frac{h}{r} | f72eb9c0ba0d1e46 | train | human | |
aP(X\ge a)\le E(X) | 1160c74b5f74daa4 | train | human | |
exp_{a}^{e}(x)=a^{a^{+^{+^{a^{x}}}}} | c2854c1bcc9a45f7 | train | human | |
\frac{(287\cdot\sqrt{207})^{8}}{(122+155)} | de12a0ac221cf02d | train | human | |
\frac{nA+x}{n+1} | ce3f070520ebd254 | train | human | |
50^{50^{50^{50^{59}}}} | f74edda374939e98 | train | human | |
exp_{v}^{n}(x)=v^{v^{-^{-^{v^{x}}}}} | 5d2f7c16989d798b | train | human | |
\frac{d(b)}{dt} | f0db4226be0b79f2 | train | human | |
\sum_{i=a}^{b}f(i) | 56a44b0128026bf9 | train | human | |
p\notin(0,1) | 169999429171e253 | train | human | |
a/\sigma_{2}=u/\sigma_{1} | 9a9d685853f9a296 | train | human | |
\tilde{\chi} | 5b8d035c8b3456cc | train | human | |
\hat{G} | 98d35f07adcea863 | train | human | |
\varphi_{x}\in A^{*} | d9705077829d869f | train | human | |
y\notin FV(N) | 243cd6d0381de664 | train | human | |
R_{ij}=-\frac{3}{2}\Delta(g_{ij}) | 911d29d55060814f | train | human | |
\tilde{P}(q,\omega) | 0b16b28bef4806fe | train | human | |
(\frac{7^{258}}{270})^{\frac{6}{50}} | 4aec48a0b87567ed | train | human | |
C_{3}^{3}(3)=\frac{16}{49} | 7ba8a633313dbcf1 | train | human | |
N\backslash S\notin W | 6821a9f0b3fd61bf | train | human | |
(\begin{matrix}1&2\\ 2&1\end{matrix}) | 37a7ddb8befcb534 | train | human | |
\frac{\partial}{\partial x} | 16c4a45988f3841d | train | human | |
\frac{1}{2}\rho(v_{\infty}^{2}-v_{w}^{2})A_{D} | 3c1c3de1763ba2c2 | train | human | |
\sum_{r=1}^{3}cos(\frac{2r\pi}{7})=\frac{-1}{2} | 2bcb3a5b0cab9e67 | train | human | |
\frac{m}{\sqrt{\frac{w^{2}}{l^{2}}-1}} | 015a92179e3f9230 | train | human | |
-\frac{\hbar^{2}}{2m}\nabla^{2} | 4546e140de727842 | train | human | |
\hat{x}-x | bd0f21ea27688089 | train | human | |
\tilde{\phi} | 9c2446153a7a45e2 | train | human | |
\prod_{p\le X}\frac{N_{p}}{p} | 2c5d601baf586fea | train | human | |
P=\frac{oz^{2}}{\sqrt{1+\frac{v^{2}}{z^{2}}}} | d26932bc17186392 | train | human | |
\{0,...,p+1\} | d515a15ef2f808f7 | train | human | |
\frac{m_{1}u_{1}+m_{2}u_{2}}{m_{1}+m_{2}} | bafaa956cc46eceb | train | human | |
2^{rel_{i}}-1 | 7f82d32f3cb2f17b | train | human | |
\frac{1}{1-e^{\frac{S\times(1-S)}{3^{N\cdot1}}}} | 9a538138be46bc0d | train | human | |
[A]_{ij}=a_{i}\cdot a_{j} | 67947827cab304b2 | train | human | |
s_{pm}=icd(w,1/\xi) | 868df0a178872d9d | train | human | |
(1+\sqrt{5})/2 | c9f7528049fd5c5f | train | human | |
\le2^{\omega} | 226e1348d778e6eb | train | human | |
\tilde{F}:=1-\frac{2M(v)}{r} | 1b9e3f390924252f | train | human | |
\tilde{A}_{2} | 8c7f6eb7e2450907 | train | human | |
\hat{S}_{a} | 5642539215c62f73 | train | human | |
x_{S}=\prod_{i\in S}x_{i} | a9e7c97e87f785f6 | train | human | |
\sqrt{\frac{\sum{D_{j}}^{2}}{w}} | d426dfe4b9e4a8be | train | human | |
C_{Cr}=\frac{U_{Cr}\times\dot{V}}{P_{Cr}} | 4cc0aa0f67493ac0 | train | human | |
P_{4}=1 | 9687d9600b659f12 | train | human | |
\sigma_{A}^{2}\sigma_{B}^{2}\ge|\langle f|g\rangle|^{2} | 819fbf86c940ea8d | train | human | |
j=\frac{j_{9}}{\sqrt{3-\frac{v^{8}}{c^{8}}}} | 5f1cd605a4a71793 | train | human | |
\frac{\frac{5}{365}}{\frac{448^{119}}{3}} | 9512c1eb07ee3e5e | train | human | |
t_{max}f_{a}^{\prime}(t_{max}) | 1283e72b24e2fed3 | train | human | |
\alpha[f]\longrightarrow\alpha[f^{\prime}] | 911758a413811973 | train | human | |
M_{\overline{m},\overline{n}} | 35335bc8a00825f8 | train | human | |
P(m_{t}|x_{t},m_{t-1},o_{t}) | f98b48d46a92d231 | train | human | |
\frac{\partial z}{\partial x}=3 | 3dee7fddc9f1116d | train | human | |
(\frac{p}{b})=(\frac{p}{B})=-1 | 9abf7b39f0ca5c6f | train | human | |
c=\sqrt{\frac{g}{k}+\frac{\sigma k}{\rho}} | b6b0262818c3576a | train | human | |
\frac{dh}{dt}=0 | 86f07fce55be0c0d | train | human | |
\frac{n(n+1)}{2}=\sum_{k=1}^{n}k | 5644a8f9cffeea9e | train | human | |
k^{k^{k^{\cdot^{\cdot^{\cdot}}}}} | 77a63618fcfac2d8 | train | human | |
\vec{p}=-g\vec{s}/||\vec{s}|| | bb9791024388fd83 | train | human | |
\frac{Z_{i1}}{R_{0}}=\frac{R_{0}}{Z_{i2}} | dac077a71727b4d7 | train | human | |
\overline{M}_{g,n}(X,A) | e3247e4756754155 | train | human | |
f(\hat{x},\theta)>f(x,\theta) | 81c0c3109aa27cd6 | train | human |
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