image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1 value | data_type stringclasses 1 value |
|---|---|---|---|---|
\lfloor\frac{(r-1)n^{2}}{2r}\rfloor | 3683127622f799bf | train | human | |
(\overline{m_{1}}) | a1789ebe76e72c94 | train | human | |
(\lambda A)_{ij}=\lambda(A)_{ij} | 328809699a07034b | train | human | |
\tilde{A}_{3} | 9b3ce14029d6b436 | train | human | |
C_{n}\sim\frac{4^{n}}{n^{3/2}} | 6cf08e0eff7370c1 | train | human | |
|e^{z}-1|\le\frac{1}{2} | d4c47beb30b19265 | train | human | |
\int p(x)dx=1 | 2f0bc589935073b1 | train | human | |
e^{38^{38^{38^{322}}}} | 12d02bd88ad27da1 | train | human | |
\frac{V_{cc}^{2}}{R_{1}} | ae096e480067a521 | train | human | |
\int_{\mathbb{R}}f(x-y)g(y)dy | 3c1020dde873873f | train | human | |
\{i,j\}\notin E | 0c6c90da29dd2adc | train | human | |
\tilde{Q_{s}} | dd3d708a6702f700 | train | human | |
x_{h}+x^{*} | 98b53d1346856878 | train | human | |
\hat{p}=1 | bf025ceed0011c1a | train | human | |
r=z\sqrt{1+\frac{\rho^{2}}{z^{2}}} | 8a0dce89aa35d932 | train | human | |
(\begin{matrix}n\\ r\end{matrix}) | 660fcbe7d6c5ec82 | train | human | |
\frac{d}{dx}[xz] | 5e04b383f3a5777c | train | human | |
\{\begin{matrix}4\\ 4\end{matrix}\} | a20269d9d3ef8198 | train | human | |
J=\int Fdt | 20419427eceef5c0 | train | human | |
K_{v}=F\sqrt{\frac{SG}{\Delta P}} | 9939263a702b3988 | train | human | |
A=\prod_{i=1}^{n}A_{i} | 778af06982131ded | train | human | |
|f(\frac{p}{q})|\ge\frac{1}{q^{d}} | aaff93234639296e | train | human | |
c^{\prime}=\sqrt{c} | e5739a2a71474a50 | train | human | |
=2p_{1}p_{2}(1-cos\theta) | 1dbca44a7f664646 | train | human | |
\overline{S_{1}} | 718888614c8fc8af | train | human | |
\hat{n}_{i} | b017dc565b2cf645 | train | human | |
1:\sqrt{\varphi}:\varphi | dfcd878ba6b7cc86 | train | human | |
c\le a+b | 815f017a743a7a70 | train | human | |
\hat{S}_{k}^{lm}(f) | 8e81ce8c4efb93d0 | train | human | |
g_{i}=\frac{\partial x}{\partial\xi^{i}} | ea1d092a855fbd0e | train | human | |
\frac{o^{+\frac{j^{2}}{2\sigma^{2}}}}{\sqrt{2\pi}\sigma} | 6fb4184910d1c2df | train | human | |
\overline{X}_{n} | 0614c1fa74dc2490 | train | human | |
\frac{\frac{5}{398}}{\frac{141^{5}}{304}} | 53e1ea8a10502f0c | train | human | |
E=\frac{fa^{4}}{\sqrt{1\cdot\frac{v^{4}}{a^{4}}}} | 3f3f6efcb2276518 | train | human | |
\prod_{t\in T}(1-x^{t})^{-1} | 3615fead24a53fad | train | human | |
\prod_{i}A_{i} | 44f1c182f7781fae | train | human | |
n+\frac{1}{3} | c8286627b9a32e76 | train | human | |
15^{15^{15^{15^{...}}}} | 03f50cc8d138d3fb | train | human | |
\{\begin{matrix}3\\ 5\end{matrix}\} | 35f5faf8cb6f6b54 | train | human | |
-\sqrt{\frac{2}{21}} | 4603118f09b903ad | train | human | |
E=\frac{fa^{4}}{\sqrt{1\cdot\frac{v^{4}}{a^{4}}}} | bd1521b84d46f363 | train | human | |
k[\overline{X}] | 8fbeebc4929b1314 | train | human | |
g=\int Gdz | f4f65c07acd58215 | train | human | |
f=\prod_{P}P^{f_{P}} | c3c438955de1d46a | train | human | |
\frac{dy}{y}=-f(t)dt | 5ba7989b2d7b0067 | train | human | |
y=\epsilon^{\frac{1}{4}}+y^{5} | c1bbbaf259431a34 | train | human | |
\tilde{C}_{n} | 870dc632de3f799d | train | human | |
S=\sqrt{L^{2}+(x+a/2)^{2}} | cf2d42a75db0f461 | train | human | |
0\le N<(\begin{matrix}n\\ k\end{matrix}) | 47ab4ee8a7eaf645 | train | human | |
lim_{x\rightarrow9}2\sqrt{x} | ec5df4b10d7443c9 | train | human | |
\nabla\times B=\frac{4\pi j}{c} | 9e8d90a5dc0ab0a5 | train | human | |
\underline{x}^{k} | 73cc9aba41650fa7 | train | human | |
\frac{470^{10}}{7+9^{5}} | 6a8146dc70215d8a | train | human | |
V_{t}=\sqrt{\frac{\mu}{r}} | b1fa833f09fdb6bb | train | human | |
\int\frac{x}{x^{2}+1}dx | 3b41b79799d4e59f | train | human | |
e_{1}>e_{2}>e_{3} | 582b8d8f5b7816e9 | train | human | |
\hat{d} | 427a279c68c370ca | train | human | |
\int_{a}^{b}f(x)dx | 84ea75bc3e7c8c7d | train | human | |
f(x)\approx x | 2c23fff132d7c09e | train | human | |
A/(2(1+\sqrt{2}))=s^{2} | 7f9f2423a4fcb6a3 | train | human | |
\frac{9}{4}-218+1^{7} | 79b0dc50a63b802e | train | human | |
\overline{X}_{1} | d67a6e07db2e87f7 | train | human | |
E(\underline{x}|y) | 6cf2d6b66906fce9 | train | human | |
\int xcos(u)du | df94efdcc401d6ba | train | human | |
|\begin{matrix}a&c\\ b&d\end{matrix}| | bfa0469a7da20d6d | train | human | |
i_{q}=\frac{1}{\frac{1}{i_{q_{0}}}+\frac{ka}{p}} | 8e1ae10a02006f35 | train | human | |
\int_{C}=0 | a6ab6e4ac7406ec3 | train | human | |
-\frac{1}{30} | 413083c6ca838422 | train | human | |
S=\frac{E[R-R_{b}]}{\sqrt{var[R-R_{b}]}} | c1ba079fe112cd22 | train | human | |
x=2azeq_{x}(\frac{\lambda}{2},\varphi) | a63f465e1c8c0c38 | train | human | |
(\begin{matrix}c_{i}\\ i\end{matrix}) | b28acc9f0af0551d | train | human | |
\hat{y}_{t} | 071274423b7d235d | train | human | |
\int_{C}x^{2}dy | 7806ae7e9988ae99 | train | human | |
\int f^{2}dP<\infty | 3255f00fb72e9080 | train | human | |
c=\frac{\partial C}{\partial m} | 6ff87d94db7c5e11 | train | human | |
p_{2}T | 5d79e4d9103e2f8e | train | human | |
(\begin{matrix}-1&-\nu\\ 0&-1\end{matrix}) | da580f870f9d70b9 | train | human | |
\frac{\partial(x,y)}{\partial(s,t)} | ce71bca4587ae14a | train | human | |
\frac{d^{2}V}{dz_{k}du_{q}}=0 | e7b1f35ffd2c2362 | train | human | |
8.4\times10^{-17}seconds | 000c731674bb23b7 | train | human | |
\frac{\frac{(8\cdot\sqrt{303})}{24}}{6^{374}\cdot7} | 02b9a2a206834244 | train | human | |
p=\frac{m\cdot v}{\sqrt{1-\frac{v^{2}}{c^{2}}}} | 77f9e577717b2c85 | train | human | |
\frac{1}{\eta}\frac{\Delta P}{\Delta x}=\frac{1}{r}\frac{d}{dr}r\frac{dv}{dr} | c3d0af05bff80fff | train | human | |
[\begin{matrix}0&0\\ 0&1\end{matrix}] | 3e037fd444681d20 | train | human | |
1+n/4r^{2} | 6881b194353d68b1 | train | human | |
\int_{S}H^{2}dA | 7d1f987868ffee07 | train | human | |
\frac{\partial u}{\partial t}=0 | fd0e49e33a70ae6c | train | human | |
\tilde{y}=\tilde{w}=h(\tilde{X})-\tilde{Y} | e5a2b5db381c4822 | train | human | |
\frac{367}{362}+324^{7} | 094805643e76fcab | train | human | |
L^{2}=\frac{N}{2}(\frac{N}{2}+1)\hbar | ebf5a9897338dd9c | train | human | |
\frac{\partial W}{\partial I_{1}}=C_{1} | 06d64f38a9f972cd | train | human | |
\frac{dX}{dt}=AX | 0093d46f4d2e5a2f | train | human | |
\frac{k}{2n+2-k} | 5975fbcfe2acb3ad | train | human | |
y=\int f(x)dx | 384864e895c65904 | train | human | |
{78^{5}}^{26-\sqrt{9}+\sqrt{360}} | 347e181d39d2eddb | train | human | |
\hat{R}_{I} | a50634a22e788df6 | train | human | |
\epsilon=\frac{T_{e,db}-T_{l,db}}{T_{e,db}-T_{e,wb}} | 160a0130b7d4328d | train | human | |
\theta=\pi/6 | 76499af16b37cbd9 | train | human | |
\frac{\frac{\sqrt{84}}{8}-206}{\frac{(6\cdot\sqrt{3})}{7}} | 7edc601ea0100a71 | train | human | |
V(r)=\frac{-\mu_{1}}{r_{1}}-\frac{\mu_{2}}{r_{2}} | ab7bdb648ab87d28 | train | human |
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