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}{M}\sum_{i=1}^{\infty}\alpha_{i}\sum_{j=0}^{i-1} | 4c5253569bd86847 | train | human | |
n^{\sigma}e^{(logn)it} | 5903fa2477449bc9 | train | human | |
x\mapsto\prod_{i=1}^{n}w_{x}(i) | c0308a86fc0aff40 | train | human | |
\rho_{R}=\frac{B^{2}-A^{2}}{2\pi G} | 0c61bda6d97d0c60 | train | human | |
k=k_{0}\sqrt{\epsilon_{r}}=k_{0}n | 4281f1dc4015a955 | train | human | |
0\le y,y^{\prime}<256^{l} | e39c01653d4525b1 | train | human | |
F=0.8 | 69f5203974d997df | train | human | |
(\frac{6}{194})^{\frac{\frac{397}{5}}{86}} | 1989fe13a22e1971 | train | human | |
(\begin{matrix}n\\ m\end{matrix}) | ac33dac4c9216bbe | train | human | |
s=\frac{1}{2}(\sqrt{5}-1)l | ab88838e57ff5004 | train | human | |
t_{c}=\sqrt{\frac{a}{c}} | 632e05b0a3fd465f | train | human | |
\frac{\sqrt{70}}{469}+(\frac{4}{10})^{304} | 4192050c02266985 | train | human | |
f^{*}J\rightarrow O_{X} | b6b1e38dea359f42 | train | human | |
\int Mds\sqrt{v} | 789a03088e8c23c6 | train | human | |
\frac{x}{y}=\frac{q}{n_{i}}+\frac{r}{yn_{i}} | 2060285294e88103 | train | human | |
|V|=|\dot{P}|=\frac{ds}{dt} | 7eb231f071b6748b | train | human | |
\frac{4}{\sqrt{4-\frac{v^{9}}{x^{9}}}} | f0b703ea6530bb73 | train | human | |
a(x)=\int f(x)dx | 8fcd56bef9096151 | train | human | |
\chi\prime=\alpha(\chi-\chi_{min}) | f35b6c54dfd66e8b | train | human | |
\frac{n(n-3)}{2} | b0dc5c88c6fc42e4 | train | human | |
\frac{1}{n^{1.07}} | fec4a579c7aef993 | train | human | |
O(\sqrt{m}) | 25eecda07240a4b9 | train | human | |
L=100\sqrt{Y/Y_{n}} | 3a029853ffc59ecc | train | human | |
(261+169+\frac{3}{24}+141) | 5490149b5a56df39 | train | human | |
\frac{1+\frac{n}{c}cos\iota_{s}}{\sqrt{1\cdot\frac{n^{3}}{c^{3}}}} | 61a879005cb12bd0 | train | human | |
c | 298f656b3507e0b3 | train | human | |
\frac{\sum_{i=1}^{n}(X_{i}-\overline{X})^{2}}{\sigma^{2}} | a2dc95955a87fe00 | train | human | |
4^{4^{+^{+^{+^{n}}}}} | a1efc8a390e8c163 | train | human | |
(\frac{a}{m})=1 | 1cd2124fedb91d77 | train | human | |
P_{n}=1^{\prime}\otimes...\otimes1^{\prime} | 67adde4f99d1a6a7 | train | human | |
O(n^{2}logn\cdot log\frac{1}{\delta}) | 04e8e9e62da64242 | train | human | |
(6\cdot361)^{8^{474}} | 79410dbd0b279674 | train | human | |
\rho(u)=\frac{1}{\sqrt{1-\frac{u^{4}}{r^{4}}}} | 8f550f2c6395df6f | train | human | |
\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{j}}=\frac{\partial L}{\partial q_{j}} | 7434f4e33a94a2ba | train | human | |
\int fdg | b35faf6c78ad22e1 | train | human | |
d=\frac{\lambda}{2NA} | 2d23eebe4eb75e17 | train | human | |
a^{-\frac{1}{3}(\frac{log\frac{x}{x_{8}}}{log\Xi})^{3}} | d99516de8d172c46 | train | human | |
(\frac{n!}{k!(n-k)!}) | 58628f0a1d362474 | train | human | |
n | d74d2a18c6429a4e | train | human | |
0\le k\le n/2+1 | 42b96928934c1feb | train | human | |
\mu=\frac{\pi}{2}\frac{m}{m_{p}} | 3d01814918704097 | train | human | |
Q(\zeta_{p^{\alpha}}+\zeta_{p^{\alpha}}^{-1}) | 1497b058319a4654 | train | human | |
w | 891d29391995385d | train | human | |
A=[\begin{matrix}a&c\\ c&b\end{matrix}] | 48c559b599ad2af2 | train | human | |
\mathbb{W} | 7764d3223030f2e4 | train | human | |
b_{\mu^{7}} | 2e084239fa198cab | train | human | |
{(\delta^{\sigma})}^{\zeta} | 65510f3353b16942 | train | human | |
f(x)=a+\frac{b}{x} | 027b48be1c307f47 | train | human | |
[A_{i},B_{j}]=0 | 03270394180b44a3 | train | human | |
x\frac{d}{dx} | 3a79f88952651e81 | train | human | |
{(w^{j})}^{1} | f66d72cd187e8e15 | train | human | |
k=\frac{\sqrt{2m(E-V)}}{\hbar} | b23d91e9741cdc6f | train | human | |
\tilde{A}_{5} | eb83fca90e7e6c7a | train | human | |
u_{e}=\frac{u_{x}}{\sqrt{\frac{u_{x}}{u_{m}}}} | 696e980ca8408dfa | train | human | |
2\sqrt{2} | dcd100dda1c19dce | train | human | |
E=\prod_{k\in G}S_{k} | a124d21e99499fc6 | train | human | |
2(\begin{matrix}n\\ j\end{matrix}) | 3f37059abebf969f | train | human | |
\sqrt{1} | f9ec709bdd1becab | train | human | |
\overline{\frac{\partial(\overline{r_{h}}\cdot r_{h}^{\prime})}{\partial x_{h}}}=0 | 0adff8f202101e24 | train | human | |
++ | 0d54a1b3c47f082f | train | human | |
\underline{a}_{1},...,\underline{a}_{r} | 91d1a634e356d76d | train | human | |
Z_{i}=\frac{\hat{p}_{i}+\overline{p}}{\sqrt{\frac{\overline{p}(5+\overline{p})}{s_{i}}}} | 22961dcb6fc960de | train | human | |
D_{C}\le D_{VC}+1 | 530a3b6226be3758 | train | human | |
\tilde{\phi}\circ\omega_{G}=\omega_{H}\circ\phi | 7d7445ed69bfaac1 | train | human | |
\frac{2\chi}{\sqrt{\frac{Um_{sen}}{o^{9}}}} | e852f6360b47f35d | train | human | |
a_{12}=\frac{\pi e^{2}}{2\epsilon_{0}m_{e}c}f_{12} | 9475b0118f3800ed | train | human | |
\varphi\vdash\psi | 6b07a522f1af934a | train | human | |
8*3!=48 | 91b65810a2986f5c | train | human | |
\prod X_{i} | c5aaf552035c8c00 | train | human | |
v=\frac{q}{\sqrt{1-\frac{p-H}{2H_{m}}}} | 307dad610cbb1605 | train | human | |
\frac{dE}{dx}=0 | 286c06934332eee4 | train | human | |
\int_{a}^{b}dx | 8d83b0a9dd56e2fb | train | human | |
\frac{10\sqrt{a}}{a} | 3006b6577abf0e50 | train | human | |
[t_{l},t_{u}]\subset T | bf1a5669d6825de0 | train | human | |
H_{n}=H_{n}^{(1)} | 7dad3e4270eed133 | train | human | |
\hat{S_{z}} | bb086ae09d65b4b2 | train | human | |
\hat{q}_{o} | 9df3d0bfce5504da | train | human | |
F_{jk}=-F_{kj} | a827642040ddbc40 | train | human | |
2((\begin{matrix}n\\ 1\end{matrix})+(\begin{matrix}n\\ 2\end{matrix})+(\begin{matrix}n\\ 3\end{matrix})) | 0816f48ddc1101d6 | train | human | |
\frac{1}{\mu_{j}}=E(S_{j}) | b6cf428691709369 | train | human | |
\overline{L_{2}} | e58676085a911a8c | train | human | |
(f,\hat{O}g)=(\hat{O}f,g) | ae493a7345b11d12 | train | human | |
\sqrt{\frac{\sum{R_{i}}^{5}}{n}} | 46e52a40e6930aeb | train | human | |
(\begin{matrix}n+r-1\\ r\end{matrix}) | 9df8612671446ca2 | train | human | |
\tilde{T}_{2}(gG^{\prime})=t_{3}^{-j}H_{2}^{\prime} | 6a75806e7f87cca1 | train | human | |
\frac{dy}{dx}=xy | 821f7ebd7cae7491 | train | human | |
\prod_{i=0}^{k-1}(x-z_{i}) | e7745a696154a752 | train | human | |
t\le\frac{n+1}{2} | 1cc373c814eafff8 | train | human | |
s\{\begin{matrix}2\\ 3\end{matrix}\} | 2bea23ba867a640b | train | human | |
(\frac{P(X_{1}^{n}(i^{\prime}))}{P(X_{1}^{n}(i))})^{s}\ge0 | 1f8a782f052a7532 | train | human | |
2(\begin{matrix}n\\ j\end{matrix}) | 13bb3af8c65abff6 | train | human | |
P=(\begin{matrix}a+1\\ 1\\ \end{matrix}) | b3f6ec01d5ae73f9 | train | human | |
S | eb82494462f06e8b | train | human | |
\frac{(491+8)^{382}}{6^{2}} | 937d6d990f95f469 | train | human | |
(\begin{matrix}n\\ a\end{matrix})<e^{at} | e3fc04d4a3ac9826 | train | human | |
\beta=c\sqrt{n} | 85ccc98eb3b9d21d | train | human | |
(d,(\begin{matrix}d+1\\ 2\end{matrix})) | a7ae36012486cf27 | train | human | |
(\begin{matrix}c_{k}\\ k\end{matrix}) | 6cd6eac377d9782c | train | human | |
\overline{w}=\frac{\partial y}{\partial w} | b99ee37ca43761ee | train | human | |
\hat{x}_{1} | 1ab42a5ad9e0331f | train | human |
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