image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1
value | data_type stringclasses 1
value |
|---|---|---|---|---|
-\int_{1/2}^{1}2\lfloor\frac{1}{x}\rfloor dx | 93da39772a2d2fbf | 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}} | 7e0c11103dc6e51c | train | human | |
\sum k(\begin{matrix}n\\ k\end{matrix}) | 2aae01dffa3be7e4 | train | human | |
\hat{\xi} | 150283c20da28a86 | train | human | |
F^{u_{u}} | 0f04c10ea8c88289 | train | human | |
\chi_{i^{t}} | 41159a9a1871435b | train | human | |
A=\frac{RT(n^{2}-1)}{3p} | d5ee4091590f7c94 | train | human | |
\partial:C_{k}\mapsto C_{k-1} | 8fbd28740c29259d | train | human | |
y=\sqrt{x^{2}-|w|^{2}}>0 | 1e78f84df88baa18 | 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 | b9cea6589e0f955f | train | human | |
(\begin{matrix}n\\ m\end{matrix}) | 90b14da2819a4de2 | train | human | |
\nu(A)=\int_{A}f_{n}d\mu | 5f7552e3865ec2a2 | train | human | |
b_{n}=\sigma log(\frac{1}{n}) | 76a0774ee0779ca2 | train | human | |
\phi=\frac{3}{2}\eta | 815a70813d9369a9 | train | human | |
\frac{(x_{i}-x)}{R_{i}} | f97d9b752bdf4b0b | train | human | |
(\begin{matrix}c_{i}\\ i\end{matrix}) | 4b10aaf9ce8921cb | train | human | |
v\sim\sqrt{\frac{kT}{m}} | f87dde71fcacde98 | train | human | |
\frac{458}{496}/475^{245} | ef8bac29eda68949 | train | human | |
L(s,\pi,r),L(s,\tilde{\pi},r) | 7908ce535567cf71 | train | human | |
\int_{a}^{b}dx | eeb7753ee20abbee | train | human | |
h_{J}\leftarrow\hat{h} | bfab61d137bc3397 | 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} | fa8c5bf54a4ba1b4 | train | human | |
\tilde{B}_{5} | 7279267ce35d95fb | train | human | |
J=\frac{500}{1+\lambda_{i}^{2}} | a33be1b9317df8ca | 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}} | b4456bfb4e3d24e3 | train | human | |
\frac{R_{f}}{R_{b}}=\frac{2A_{0}+3}{A_{0}-3} | 582885cd9a701881 | train | human | |
x,y\in[x] | 37351c89df849613 | train | human | |
{78^{5}}^{26-\sqrt{9}+\sqrt{360}} | f2e0620ce965d150 | train | human | |
P=\frac{U}{3V}=\frac{\epsilon\sigma T^{4}}{3V} | 29a3a4d2fde2777e | train | human | |
\mathbb{Z}[\sqrt{-3}] | 2d8f2d7cff08c530 | train | human | |
-\sqrt{c} | 85a3e4c5080aa079 | 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} | c8a8dd86708d8df8 | train | human | |
A=B^{-T} | 0f75264f1d0591dc | train | human | |
(\begin{matrix}p+q\\ p\end{matrix}) | 3650a4eb023ec6a2 | train | human | |
5^{5^{5^{5^{5^{5}}}}}-7 | a3eb5244c78fa89b | train | human | |
\alpha_{p}=\frac{1}{V}(\frac{\partial V}{\partial T})_{p} | 0e57f1967c325ea1 | train | human | |
p\approx\frac{ln2}{365} | 08a6f878347e8da6 | train | human | |
Q_{j,x}=\int y_{i}dA | 1af1a00f52e06508 | train | human | |
\Phi[A]=\hat{O}\Psi[A]Eq1 | 4a7f02ecdea1a6ed | train | human | |
\frac{\partial Q}{\partial t}+V_{w}\frac{\partial Q}{\partial x}=0 | a93d50929d12b32f | train | human | |
\frac{\partial f}{\partial x}(0,0)=0 | e454a983e3fdfa4a | train | human | |
Q,Q\notin P | 4d9e042034c7dbab | train | human | |
\overline{\frac{\partial(\overline{t_{i}}-t_{i}^{\prime})}{\partial x_{i}}}=2 | 514912b56e14abb2 | train | human | |
\frac{d}{d\tau} | 7c968a9a2280d649 | 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}] | 2d785c4fdb8196ec | train | human | |
a_{x}=\frac{8eU}{mr_{0}^{2}\Omega^{2}}(10) | 0a4f210197177e23 | train | human | |
R^{2^{N}} | 701906abbea6460a | train | human | |
\frac{\partial u}{\partial t}=0 | bc4b22afdd43fb5f | train | human | |
D_{n}=4n^{2}-3n | 19a7b6519402264c | train | human | |
\frac{1}{2}I\omega^{2} | ea05b2519e99b511 | 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 | 8128ee4b5ffb7874 | train | human | |
\sqrt{V} | f6d93f532992b6c1 | train | human | |
B_{ik} | ae13afa07fbe0093 | train | human | |
log\frac{1}{1-z}=\sum_{k\ge1}\frac{z^{k}}{k} | 8cf80c2668b63a50 | train | human | |
\int d^{3}xJ^{0} | 0d272a0579503ca8 | train | human | |
\int_{S}\omega=\int_{T}d\omega | 3965cc5fd1e64d3c | 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}}} | 5da33dd24112d329 | train | human | |
\frac{128}{125} | 12180bb32510278b | train | human | |
2N^{2}/h+\sqrt{\pi N^{3}h} | 4dbe35549e84f18d | 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 | 76aa7c0efeb1f6f2 | train | human | |
z^{\prime}=c+(z-c)e^{i\theta} | 053885b0f108f7da | train | human | |
u=\prod_{i=1}^{k/2}p_{i} | b7fa8ae37b10ca48 | train | human | |
\rho\propto a^{-3}=V^{-1} | 29a7ebfa23daf0e5 | train | human | |
(A^{g}A)^{T}=A^{g}A | 5202f3fd4c26feb5 | train | human | |
a^{-b}=\frac{1}{a^{b}} | 2584d4b02ceac6d5 | train | human | |
(\begin{matrix}i\\ j\end{matrix}) | 0ba9eeed87192368 | train | human | |
\Omega(x)=\frac{e^{-\frac{x^{1}}{1}}}{\sqrt{1\Lambda}} | 01a50ea1699481d9 | train | human |
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