image
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4
512
latex
stringlengths
1
188
sample_id
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16
16
split_tag
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1 value
data_type
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1 value
-\int_{1/2}^{1}2\lfloor\frac{1}{x}\rfloor dx
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train
human
L^{2}[0,1]
32f7cf716351471d
train
human
c_{n}=\frac{1}{n}\sum_{i=1}^{n}a_{i}
879d29f05b56fa24
train
human
(x+y)^{n}=\sum_{k=0}^{n}(\begin{matrix}n\\ k\end{matrix})x^{n-k}y^{k}
27d4f521104da70f
train
human
\int_{S}FdS
38506f65e0689573
train
human
|\frac{\omega(p)}{p}|\le10^{-14}
5aa062350fc1dd3f
train
human
\frac{I_{3}}{\sigma_{xx}\sigma_{yy}-\sigma_{xy}^{2}}
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train
human
\sum k(\begin{matrix}n\\ k\end{matrix})
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train
human
\hat{\xi}
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train
human
F^{u_{u}}
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train
human
\chi_{i^{t}}
41159a9a1871435b
train
human
A=\frac{RT(n^{2}-1)}{3p}
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train
human
\partial:C_{k}\mapsto C_{k-1}
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train
human
y=\sqrt{x^{2}-|w|^{2}}>0
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train
human
n!=\prod_{k=1}^{n}k
ace2b52e2c6093a5
train
human
(\frac{386}{\sqrt{307}})^{6}\cdot363^{9}+404
6718bde3371774c4
train
human
\int p(x)f(x)dx=-H
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train
human
(\begin{matrix}n\\ m\end{matrix})
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train
human
\nu(A)=\int_{A}f_{n}d\mu
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train
human
b_{n}=\sigma log(\frac{1}{n})
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train
human
\phi=\frac{3}{2}\eta
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train
human
\frac{(x_{i}-x)}{R_{i}}
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train
human
(\begin{matrix}c_{i}\\ i\end{matrix})
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train
human
v\sim\sqrt{\frac{kT}{m}}
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train
human
\frac{458}{496}/475^{245}
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train
human
L(s,\pi,r),L(s,\tilde{\pi},r)
7908ce535567cf71
train
human
\int_{a}^{b}dx
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train
human
h_{J}\leftarrow\hat{h}
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train
human
(\frac{\alpha}{\beta})_{m}=1
01a56167b5a07cac
train
human
(\begin{matrix}a\\ b\end{matrix})
c271567893513470
train
human
j(z_{v})
4c99bafdfed2479b
train
human
(\frac{9}{2})^{\sqrt{129}^{\sqrt{119}}+1}
b8db97b56711fe2e
train
human
R(w)=\frac{1}{2\eta}||w||_{2}^{2}
471a3168bc3c088c
train
human
\sqrt{\psi}
b5fa0fe42bba97f1
train
human
\omega^{\frac{M_{p}+1}{2}}
96a16af2f5a0b96a
train
human
(\begin{matrix}n\\ t\end{matrix})
67288fa87c0058af
train
human
(\begin{matrix}i&-1\\ i&1\end{matrix})
bd1c68541becb79a
train
human
\langle z,w\rangle=\sum_{n=1}^{\infty}z_{n}\overline{w_{n}}
85c0e13d7fec7e18
train
human
C:X\rightarrow[0,+\infty]
418e2f8d6a25cc50
train
human
\phi:[-\tau,0]\rightarrow R^{n}
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train
human
\tilde{B}_{5}
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train
human
J=\frac{500}{1+\lambda_{i}^{2}}
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train
human
\frac{\frac{\frac{238}{9}}{4}}{6-248-5}
b524a3a726b9ae95
train
human
var_{GX}=e^{var[lnX]}
f3a4b97b162a6f14
train
human
(\begin{matrix}11\\ 5\end{matrix})
d4ef91c9f8a56f38
train
human
\int_{0}^{\infty}f(x)dx
d9409c57137bca81
train
human
u_{0}^{2}\approx u_{n}u^{n}=\frac{u_{n}^{2}}{c^{2}}
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train
human
\frac{R_{f}}{R_{b}}=\frac{2A_{0}+3}{A_{0}-3}
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train
human
x,y\in[x]
37351c89df849613
train
human
{78^{5}}^{26-\sqrt{9}+\sqrt{360}}
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train
human
P=\frac{U}{3V}=\frac{\epsilon\sigma T^{4}}{3V}
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train
human
\mathbb{Z}[\sqrt{-3}]
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train
human
-\sqrt{c}
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train
human
\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}-\frac{\partial L}{\partial x}=F
223b824edb6fd17c
train
human
-\frac{\partial\phi}{\partial x}
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train
human
A=B^{-T}
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train
human
(\begin{matrix}p+q\\ p\end{matrix})
3650a4eb023ec6a2
train
human
5^{5^{5^{5^{5^{5}}}}}-7
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train
human
\alpha_{p}=\frac{1}{V}(\frac{\partial V}{\partial T})_{p}
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train
human
p\approx\frac{ln2}{365}
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train
human
Q_{j,x}=\int y_{i}dA
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train
human
\Phi[A]=\hat{O}\Psi[A]Eq1
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train
human
\frac{\partial Q}{\partial t}+V_{w}\frac{\partial Q}{\partial x}=0
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train
human
\frac{\partial f}{\partial x}(0,0)=0
e454a983e3fdfa4a
train
human
Q,Q\notin P
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train
human
\overline{\frac{\partial(\overline{t_{i}}-t_{i}^{\prime})}{\partial x_{i}}}=2
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train
human
\frac{d}{d\tau}
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train
human
V(x)=\frac{1}{2}kx^{2}
072b82a0d1c1786b
train
human
{344^{2}}^{\frac{343^{228}}{9}}
fc4afbd171c0417d
train
human
[\begin{matrix}p&t\\ q&u\end{matrix}]
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train
human
a_{x}=\frac{8eU}{mr_{0}^{2}\Omega^{2}}(10)
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train
human
R^{2^{N}}
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train
human
\frac{\partial u}{\partial t}=0
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train
human
D_{n}=4n^{2}-3n
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train
human
\frac{1}{2}I\omega^{2}
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train
human
\theta=\frac{arctan\frac{c}{b-a}}{2}
d1980e8a2f3cdc2c
train
human
E||\theta-\hat{\theta}||^{2}
019c1ebe7df5e841
train
human
N\int BdS=LI
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train
human
\sqrt{V}
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train
human
B_{ik}
ae13afa07fbe0093
train
human
log\frac{1}{1-z}=\sum_{k\ge1}\frac{z^{k}}{k}
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train
human
\int d^{3}xJ^{0}
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train
human
\int_{S}\omega=\int_{T}d\omega
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train
human
\frac{dS}{dt}-\frac{\dot{Q}}{T}\ge0
5bea3f1f354874c0
train
human
\tilde{f}:X\rightarrow M_{f}
d71fb8dac2e8043c
train
human
\sqrt{1-\frac{b^{2}}{a^{2}}}
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train
human
\frac{128}{125}
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train
human
2N^{2}/h+\sqrt{\pi N^{3}h}
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train
human
|\Omega|=\frac{d\theta}{dt}=\omega
ee5dc8fc9f9d1f68
train
human
\tilde{C_{n}^{m}}=-\frac{C_{n}^{m}}{\mu R^{n}}
a49b45418662dc78
train
human
lim\int_{0}^{1}f_{n}=0
2d703e8c69b242aa
train
human
S_{21}\equiv\frac{p_{2}c_{2}}{p_{1}c_{1}}
dad4bfa58f83bad6
train
human
[\omega]^{\omega}\rightarrow Q
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train
human
z^{\prime}=c+(z-c)e^{i\theta}
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train
human
u=\prod_{i=1}^{k/2}p_{i}
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train
human
\rho\propto a^{-3}=V^{-1}
29a7ebfa23daf0e5
train
human
(A^{g}A)^{T}=A^{g}A
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train
human
a^{-b}=\frac{1}{a^{b}}
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train
human
(\begin{matrix}i\\ j\end{matrix})
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train
human
\Omega(x)=\frac{e^{-\frac{x^{1}}{1}}}{\sqrt{1\Lambda}}
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train
human