image
imagewidth (px) 4
512
| latex
stringlengths 1
188
| sample_id
stringlengths 16
16
| split_tag
stringclasses 1
value | data_type
stringclasses 1
value |
|---|---|---|---|---|
(x+y)^{n}=\sum_{k=0}^{n}(\begin{matrix}n\\ k\end{matrix})x^{n-k}y^{k} | 85030eb74bcae651 | train | human |
|
(X,ln|X|) | 70d009065eaab06c | train | human |
|
f(x_{i})=\overline{y} | 0db79f1128f98168 | train | human |
|
q=\frac{V}{R}=\frac{\alpha m_{0}}{R} | 6181984dfab934ad | train | human |
|
|00z^{\prime}\rangle+|11z^{\prime}\rangle | 1d37e4ccc0872030 | train | human |
|
X_{ip}\omega_{r}cos(\omega_{r}t) | d8fd2a0028216ab7 | train | human |
|
nH(p)-o(n) | fba5bc9a7f0d5944 | train | human |
|
R_{E}=c/\sqrt{4\pi G\rho} | 81efacfecdc82573 | train | human |
|
q=\frac{z}{\sqrt{4\cdot\frac{e\cdot P}{2P_{m}}}} | c890bc7b36ef4838 | train | human |
|
\overline{Y}_{x} | 364b36d2a01ba1f7 | train | human |
|
A\underline{\delta}_{\Phi}B | bb79b463aedbe087 | train | human |
|
\sqrt{\frac{12}{35}} | 74f5a5a01a9ce891 | train | human |
|
(\begin{matrix}8\\ 4\end{matrix}) | 7f2cebadc5ffd7a3 | train | human |
|
\frac{p}{2-p} | 864d8d852fa6d318 | train | human |
|
\sqrt{\frac{\alpha\lambda}{\beta}}(x-\mu) | cebc2f626389efc2 | train | human |
|
[a,y^{2}]=[a,y]^{1+y} | 8646cd61da8a410b | train | human |
|
\hat{R} | bce423d111ce4c7e | train | human |
|
e^{it\mu}\frac{\pi st}{sinh(\pi st)} | bf8ee597609d0083 | train | human |
|
z_{0}:=M^{-1}r_{0} | 0ba55bccd233c151 | train | human |
|
C_{v_{1}}^{S}=\frac{1}{\epsilon_{S}^{2}-\epsilon_{S}^{1}} | 2747778ac5e6f63c | train | human |
|
L(x)=cothx-\frac{1}{x} | eb8b2b27b256b8b4 | train | human |
|
\frac{1}{\mu_{0}\epsilon_{0}}=c_{0}^{2} | 0c31704cc562e24f | train | human |
|
\overline{X_{t}} | 3c917d11dcc427bb | train | human |
|
\sqrt{\Theta} | 902451023667404f | train | human |
|
\prod_{p}f(p) | e10729cf5c128307 | train | human |
|
\lambda=\frac{D_{x}\Delta t}{2\Delta x^{2}} | 96693bedacdaff4c | train | human |
|
\sqrt[55]{2} | ac6a296da31fc489 | train | human |
|
1-\frac{1}{n} | 4b10cb0372bc01f4 | train | human |
|
NPV=\sum_{n=0}^{N}\frac{C_{n}}{(1+r)^{n}}=0 | d68205cd343d6914 | train | human |
|
(h_{o})_{k}=h_{2k+1} | 4ee0dfca696a0a24 | train | human |
|
x\mapsto\prod_{i=1}^{n}u_{x}(i) | 88671e3e8d16672f | train | human |
|
f(z)=\frac{4}{1-z^{4}} | 54615a9b30099f16 | train | human |
|
(S,\Phi) | c2db321bd0002e63 | train | human |
|
\frac{\frac{340}{7}}{169-1^{6}} | 475dcb1b52442873 | train | human |
|
(c/n)cos(\psi) | afe4bf7e1f93c5be | train | human |
|
\overline{Y}_{x} | 9ea28789c698bb14 | train | human |
|
\hat{U} | 4b6a94d9ae6cba5f | train | human |
|
r_{xg}=\frac{\overline{xg}}{\sqrt{\overline{x^{5}}\overline{g^{5}}}} | 57ab39de1c59882e | train | human |
|
\int\frac{sinx}{x}dx | 8dabc1179d607d73 | train | human |
|
\frac{d}{dt}N_{2}=-c_{1}N_{1} | cd653ae706cda98e | train | human |
|
E/V=K_{1}sin^{2}\theta | 6efddb903b88a6af | train | human |
|
\frac{1/468}{156/10-9} | 1d0233eeb51b939f | train | human |
|
(\begin{matrix}n\\ 2\end{matrix})^{-1} | 939431199fa5bd81 | train | human |
|
(\hat{B}_{\omega}^{\dagger}) | e84e34d8a676841a | train | human |
|
q=\frac{j}{\sqrt[4]{-\frac{d_{3}}{8}}} | 430220d279b16f8b | train | human |
|
(\begin{matrix}n-1\\ i\end{matrix}) | 45dc107fe07991db | train | human |
|
n=\sqrt{2+2k} | 39ece14e61ceb55f | train | human |
|
g^{\prime\prime}=\frac{n-1}{n^{2}}g^{-\frac{n+1}{n-1}} | f8c78c77d370e78c | train | human |
|
O(n\sqrt{loglogn}) | 21f02887f58fa8fb | train | human |
|
\tilde{Y_{k}} | bff3e85a3d38f1c8 | train | human |
|
mE-\frac{P^{2}}{2}=\frac{-P^{2}}{2} | d5fd7859a1228e85 | train | human |
|
(\begin{matrix}S-1\\ D-1\end{matrix}) | c5a42ac3e0287297 | train | human |
|
\sqrt{\frac{p}{n-p}}\approx\sqrt{\frac{p}{n}} | 4ded36df84d276b1 | train | human |
|
\vec{v}_{f}=\frac{1}{q}\frac{\vec{F}\times\vec{B}}{B^{2}} | 2413ed86d90fc66f | train | human |
|
\psi(t)=\frac{1}{\pi}\frac{1-t^{2}}{(1+t^{2})^{2}} | 8431e05ecad58363 | train | human |
|
P^{\alpha\dot{\beta}}=T^{\alpha\dot{\beta}} | e6b3ff761f69da4c | train | human |
|
E_{i}=\int E(t)dt | 47ed8f52e18775d3 | train | human |
|
\frac{\partial x}{\partial t} | 1b38b1352a677db3 | train | human |
|
L_{1}=\frac{1}{3}p_{1} | 4e428fbf0058268f | train | human |
|
\frac{1}{2}(1-\frac{\epsilon}{3}) | 1bf4f72048d1a01a | train | human |
|
\int_{-1}^{1}x^{-1}dx | c59a853c40aa2759 | train | human |
|
\int_{0}^{t}p^{\prime}(s)p(t-s)ds | 80329cd3304f7663 | train | human |
|
\hat{S}_{N}\subset C | 99f0f153251bddb3 | train | human |
|
x | 93d9e24a822b4d0f | train | human |
|
p_{4}=\frac{m_{2}}{1+m_{2}} | 23a70a4c5f1719a6 | train | human |
|
(10^{423}-3)+\frac{\sqrt{136}}{5} | eff31cc1f89e6911 | train | human |
|
R_{0}=\sqrt{x^{2}+y^{2}+z^{2}} | 25ef5336de1f824b | train | human |
|
\frac{262\cdot340}{6^{5}} | 8c4b867f83fbfc11 | train | human |
|
\int xsdx=\frac{1}{3}s^{3} | 7d84a86cdd8e51ca | train | human |
|
k=\frac{2\sqrt{2}M\Gamma\gamma}{\pi\sqrt{M^{2}+\gamma}} | 660924893897c400 | train | human |
|
\forall x\in N.x\div0=0 | ab2e0d4d3be5a9d3 | train | human |
|
2(\begin{matrix}n\\ k\end{matrix}) | e7043a8c8d22faaf | train | human |
|
S=-mc\int ds | 751e46a02674e507 | train | human |
|
\frac{1\cdot394^{5}}{\frac{\frac{7}{272}}{177}} | b8d4d78aa9149d2f | train | human |
|
{\sqrt{6}+333^{10}}^{{9^{140}}^{10}} | 6baf6f43f8af0ce7 | train | human |
|
\int_{0}^{t} | 9e5887053472eebc | train | human |
|
s\{\begin{matrix}6\\ 3\end{matrix}\} | feba6c80d7f2fe76 | train | human |
|
[\begin{matrix}12&12&123&124\\ \end{matrix}] | 4ad62408c3d46696 | train | human |
|
M=\prod_{n}c_{n} | 1f646b9fb0368c0e | train | human |
|
x_{n}e^{i2\pi nl/N} | 09b4ef96910e3058 | train | human |
|
(\frac{7\cdot99}{9})^{1^{61}} | 25ebc539374259cf | train | human |
|
s\{\begin{matrix}4\\ 3\end{matrix}\} | 565e4e2b08d7cc7d | train | human |
|
(\begin{matrix}4\\ 2\end{matrix})=6 | 766502bddb5f5ff2 | train | human |
|
(\begin{matrix}10\\ 2\end{matrix})=45 | dac48a1978788385 | train | human |
|
\frac{\partial f}{\partial x_{j}}(x) | 0005cd98bb3e2d89 | train | human |
|
\frac{d}{dt}N_{2}=-c_{1}N_{1} | 71b8d9f869bf2aba | train | human |
|
s\{\begin{matrix}3\\ 4\end{matrix}\} | 515780ebaf5f6511 | train | human |
|
\frac{(1-f)(r-1)S_{k}}{sp} | ba707643ed749fd4 | train | human |
|
\sigma=constant\cdot\frac{Z^{n}}{E^{3}} | c47267342123eae2 | train | human |
|
\frac{a}{6}(2+\sqrt{2}) | 59409f19094f4dfb | train | human |
|
\overline{z}^{n} | 8161fbccc53b1f47 | train | human |
|
x=\frac{2m-6}{m} | bd449f8e099a51b6 | train | human |
|
1/\sqrt{8\pi} | 216d1ba2d25d46e5 | train | human |
|
\int_{0}^{1}g_{n}=1 | 2934bdcb237323ee | train | human |
|
A\overline{D} | 0b73b8ff672793c8 | train | human |
|
\prod_{n=1}^{\infty}(1+p_{n}) | 036beb4cd0fa4673 | train | human |
|
\tilde{C_{n}^{m}}=-\frac{C_{n}^{m}}{\mu R^{n}} | 73309d50f9780c4d | train | human |
|
\omega_{1}=\omega_{0}\sqrt{1-\zeta^{2}} | 5c6d79cd9ae0dc80 | train | human |
|
\hat{x}\hat{y} | b00cfabc62669312 | train | human |
|
k:\hat{A}\rightarrow Prim(A) | 86396001cf2b7942 | train | human |
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