image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1 value | data_type stringclasses 1 value |
|---|---|---|---|---|
g=\frac{g_{0}}{({1+\frac{v^{6}}{c^{6}})}^{9/6}} | 641253913424c350 | train | human | |
\sqrt{-i} | a6fe3be99d25ec6f | train | human | |
k_{B}T=\frac{m\overline{v^{2}}}{3} | 151569a1568b9d7c | train | human | |
\hat{A}_{n,\alpha}^{\dagger} | 8e69c7909cbc0cdd | train | human | |
{d^{\chi}}^{m} | 29b9a9f32e660595 | train | human | |
\neg\psi\vee\neg\varphi | 3554385faafc0725 | train | human | |
nDCG_{p}=\frac{DCG_{p}}{IDCGp} | a1c698e65fb9d28c | train | human | |
\overline{1^{1/N}}=1^{-1/N} | 8380afe6ac62c3eb | train | human | |
\overline{X_{j}} | 0fbf0a298a8faa9d | train | human | |
y=f(x)=\frac{a+bx}{c+dx} | bd3b94d14340348c | train | human | |
D(n)=\sum_{k=0}^{n}(\begin{matrix}n\\ k\end{matrix})^{2}2^{k} | fbd7fc1d92f768b9 | train | human | |
(y^{\prime}(0),y(0))=(1,0) | a12c877657dd1435 | train | human | |
\hat{z}(t) | dd90d388cdd4d995 | train | human | |
\sqrt{nN} | b0c1fd90271e6a13 | train | human | |
lim_{n\rightarrow\infty}\frac{N(A,n)}{n} | 52d21367cf412ae8 | train | human | |
\sqrt{2} | 58c2bfc5c52ca071 | train | human | |
\prod_{p\le X}\frac{N_{p}}{p} | 6a78837b128374e2 | train | human | |
\frac{5^{500}}{7}+(5\cdot8)/\sqrt{170} | 317cc88cd6f45ea9 | train | human | |
V_{s}\sqrt{n} | 417914ca643c0921 | train | human | |
\frac{sin\alpha}{\sqrt{2-sin^{2}\alpha}} | d467f1a135d8b6f7 | train | human | |
x^{x^{x^{+^{+^{+}}}}} | 8cd0c97d9f8e2175 | train | human | |
\Delta_{P2} | 5cb1c093c6fd1738 | train | human | |
K=\frac{L_{H}-L_{L}}{L_{H}} | 5dcfc763404c7a54 | train | human | |
\forall p\forall x(x\notin p) | 206a0f94e047fc00 | train | human | |
p=\prod_{i=1}^{n}p_{i} | 8aef083ee1450d0c | train | human | |
q=[\begin{matrix}u\\ d\end{matrix}] | 180f9354d8e1c538 | train | human | |
E=\frac{1}{4\pi\epsilon_{0}}\frac{q}{r^{2}}\hat{r} | a43d4dfbbc2f1e04 | train | human | |
\int dx=x+C | 636daa83082519ac | train | human | |
e=\frac{1}{1+\delta} | b08653b68adf3277 | train | human | |
H_{0}(x)=\frac{e^{-x^{2}/2}}{\sqrt{2\pi}} | ea77559fe85c1ad2 | train | human | |
\hat{v}_{k} | 412fd4ce943eb0f8 | train | human | |
\frac{\frac{99}{6}}{\frac{147}{4}-94} | 806ba936abccbcf4 | train | human | |
\beta=\frac{0}{\sqrt{\sum_{\upsilon=0}^{s}\frac{j^{2}}{v_{\upsilon}^{2}}}} | a7b081ca535778c7 | train | human | |
\tilde{P}_{*} | 8e256840cca52e5b | train | human | |
\frac{q^{2}}{4}+\frac{p^{3}}{27}<0 | c36b9618581f0ef5 | train | human | |
M[\cdot]:=D(F\circ G)[\cdot] | 8852ce7bdc6e850c | train | human | |
\frac{1}{\sqrt{1-\delta}} | 3d4df931c2a0fd68 | train | human | |
c=\sqrt{n} | 210fdbf631e8aff6 | train | human | |
\zeta(-3)=\frac{1}{120} | 5e204ab7492190ea | train | human | |
\hat{\eta} | 531a628526164261 | train | human | |
\frac{\partial u_{i}}{\partial x_{i}}=0 | cd941aae3bf35840 | train | human | |
\frac{|F_{m}|}{L}=\frac{\mu_{0}}{2\pi}\frac{|I|^{2}}{|r|} | 8aa02fe9d15899fc | train | human | |
\overline{X}_{0} | cff2e78e61bcdaf0 | train | human | |
\gamma=\frac{5}{3}\approx1.67 | fd31bf0834785cdb | train | human | |
j^{l}=N_{L/K}(A)O_{K} | 1a7808a01e74d27b | train | human | |
a_{c}^{3}=\frac{9R^{2}\gamma\pi}{4E^{*}} | 59b2ccbc825c23b4 | train | human | |
|(-x)^{-x}|=\frac{1}{|x^{x}|} | 8b5fe44f5c5d5197 | train | human | |
n_{1},n_{2},n_{3} | 5b29670040061282 | train | human | |
\frac{(4+285-95)}{\frac{\frac{360}{500}}{41}} | f910659390d8eba2 | train | human | |
ye^{2\pi ix/10} | 6de84bf8dcc23c7a | train | human | |
\frac{\frac{268+7}{236}}{88^{\sqrt{347}}} | ff0cd9577dd89425 | train | human | |
{{7^{5}}^{4}}^{(\frac{6}{101})^{6}} | 6ec1e54cd667899e | train | human | |
\tilde{B}_{6} | 504f2c45b5b9d3bd | train | human | |
(\begin{matrix}r1\end{matrix})(\begin{matrix}r-11\end{matrix}) | d7e562ea81ac45a7 | train | human | |
2Y\dot{\varphi}_{r} | adabb3dfd9a670fe | train | human | |
(A+B\sqrt{C})^{n} | fba524c486089ff8 | train | human | |
\overline{x}=\sigma_{\overline{x}}^{2}\sum_{i=1}^{n}x_{i}/\sigma_{i}^{2} | 07f6ab1d6929f881 | train | human | |
a\odot b=\frac{a}{b}+\frac{b}{a} | b428006b606c67b9 | train | human | |
Q=\int j_{0}a^{3}d^{3}x | b9e5951e10bcd8ac | train | human | |
\sum_{i,j}a_{ij}x^{i}y^{j} | 345e371b1e70fc75 | train | human | |
\tilde{d}=\frac{gcs}{\sqrt{\frac{g_{7}g_{2}}{g_{7}\cdot g_{2}}}} | 909e712d4fade984 | train | human | |
A\underline{\delta}B | aef0251929e8b3c8 | train | human | |
\frac{2rect(\frac{\nu}{2})}{\sqrt{1-\nu^{2}}} | 42c079d4931eefef | train | human | |
x<\frac{1}{3}log(\frac{4}{3D}) | 492a886114eba46e | train | human | |
\int_{0}^{1}n(x)dx | 7c0bdd09ef43a215 | train | human | |
h\le(\begin{matrix}k+l\\ k\end{matrix}) | afed1e6792575024 | train | human | |
\prod_{i=1}^{n}a_{i,\sigma_{i}} | c4b2e1ac71cb261b | train | human | |
T\Delta S_{int}-Q\ge0 | 21ec2853a2326fbd | train | human | |
\sigma=\int\rho ds | 2b2b5068a926ba1f | train | human | |
\frac{\sqrt{157}}{394}\cdot(90\cdot1) | 94dbe596ee769390 | train | human | |
B=[\begin{matrix}1&0\\ 0&0.6\\ 0&0.8\end{matrix}] | a694396596760a86 | train | human | |
\frac{e^{\cdot\frac{x^{8}}{8\sigma^{8}}}}{\sqrt{8\vartheta}\sigma} | 7108a4630cd79081 | train | human | |
d=r_{1}+r_{2} | 22dbf134127b7e57 | train | human | |
\tilde{N} | 38470bb62b16de82 | train | human | |
0=MU_{x}+MU_{y}\frac{dy}{dx} | 3c9bc7b4884ac348 | train | human | |
\prod_{j=1}^{s}[\frac{a_{j}}{b^{d_{j}}},\frac{a_{j}+1}{b^{d_{j}}}] | 55afcdd95d012335 | train | human | |
\tilde{u} | ff0450ad5310e297 | train | human | |
R^{2^{n}-1} | cc7857615ff2c20f | train | human | |
\int_{Q}r^{2}dm | 2b76a6869090fe60 | train | human | |
\hat{r}_{j} | f0d746d47f3632f1 | train | human | |
\sqrt{17} | ae647011f48b4dac | train | human | |
R_{E}=c/\sqrt{4\pi G\rho} | e7ab385e6aa70946 | train | human | |
v=\frac{|a-b|}{2} | 8ce90c2a46c45d2a | train | human | |
t^{\prime}=t-\frac{|r-r^{\prime}|}{c} | a71618ea9589f40d | train | human | |
U=\int f(v)E(v)dv | fffe3427cfe7a245 | train | human | |
\frac{a_{i}}{a_{j}} | 4e40ef6762e53c24 | train | human | |
\tilde{C}_{7} | b4ab238b5f63411f | train | human | |
n\le\frac{N-1}{2} | 3254c4411257f8c1 | train | human | |
\infty\notin A | ed89243d680430a0 | train | human | |
\sqrt{2/(N-1)} | aa7bc9304e7fb839 | train | human | |
m\frac{d^{2}x}{dt^{2}}+kx=0 | 86c9d839249ce7bd | train | human | |
\epsilon=\cdot\frac{log\frac{\tau_{\lambda_{1}}}{\tau_{\lambda_{9}}}}{log\frac{\lambda_{1}}{\lambda_{9}}} | 419b34f8f9f5e039 | train | human | |
M_{i}(n)=\prod_{j=1}^{n}\mu_{i}(j) | b68dc060f01b2f5a | train | human | |
T_{L}=\frac{T_{N}}{cos(\theta)} | 0475485f18919d3f | train | human | |
\sqrt{390}^{\sqrt{7}}+\frac{6}{\sqrt{10}} | 1d581145a563067f | train | human | |
\gamma=2+\frac{k_{0}+a}{m} | 2fb9a4d9a34963db | train | human | |
\sqrt{\langle x,x\rangle}=||x||_{p} | f2a591a2ddc0aa24 | train | human | |
\tilde{C_{n}^{m}}=-\frac{C_{n}^{m}}{\mu R^{n}} | c0f21ea9026c3012 | train | human | |
r=a\frac{sin(-\theta+\theta_{0})}{sin(-2\theta+\theta_{0})} | 648a823dc6117269 | train | human | |
k=\Omega(\sqrt{nlogn}) | e7b9fa2486d9cc01 | train | human |
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