Split (3)

train · 230k rows

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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