Datasets:
image imagewidth (px) 1k 1.1k | id stringlengths 6 6 | source stringclasses 1
value | domain stringclasses 1
value | layout stringclasses 4
values | variant stringclasses 1
value | background stringclasses 3
values | n_formulas int64 4 11 | width int64 1k 1k | height int64 282 1.86k | order_spec stringclasses 4
values | prompt stringclasses 4
values | answer stringlengths 42 460 | target_plain stringlengths 31 440 | formulas listlengths 4 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
105843 | human | handwriting | numbered | photo | lines | 5 | 1,000 | 825 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\frac{\partial r_i}{\partial\beta_j}=-X_{ij}$
2) $\langle d(x,\hat{x})\rangle$
3) $[M+Na]^{+}$
4) $\Sigma_i=\gamma_{5i}\beta_i\gamma_{\perp i}$
5) $\begin{pmatrix}0&1\\-1&-1\end{pmatrix}$ | \frac{\partial r_i}{\partial\beta_j}=-X_{ij}
\langle d(x,\hat{x})\rangle
[M+Na]^{+}
\Sigma_i=\gamma_{5i}\beta_i\gamma_{\perp i}
\begin{pmatrix}0&1\\-1&-1\end{pmatrix} | [
{
"order": 1,
"latex": "\\frac{\\partial r_i}{\\partial\\beta_j}=-X_{ij}",
"bbox": [
94,
44,
624,
282
]
},
{
"order": 2,
"latex": "\\langle d(x,\\hat{x})\\rangle",
"bbox": [
94,
322,
351,
400
]
},
{
"order": 3,
"latex": ... | |
125839 | human | handwriting | stack | photo | white | 4 | 1,000 | 876 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $p(k)=\frac{\lambda^k}{k!}e^{-\lambda}$
$\int pdq=nh$
$f^{(w_j)}$
$\frac{E(1-\nu)}{(1+\nu)(1-2\nu)}$ | p(k)=\frac{\lambda^k}{k!}e^{-\lambda}
\int pdq=nh
f^{(w_j)}
\frac{E(1-\nu)}{(1+\nu)(1-2\nu)} | [
{
"order": 1,
"latex": "p(k)=\\frac{\\lambda^k}{k!}e^{-\\lambda}",
"bbox": [
48,
51,
663,
279
]
},
{
"order": 2,
"latex": "\\int pdq=nh",
"bbox": [
48,
306,
278,
415
]
},
{
"order": 3,
"latex": "f^{(w_j)}",
"bbox": [... | |
181462 | human | handwriting | numbered | photo | white | 7 | 1,000 | 1,564 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\int_0^asinxdx$
2) $f(x,t)=t\cdot x$
3) $v=D\int idt$
4) $lim_{N\rightarrow+\infty}h_N=0$
5) $\frac{3}{2}\sqrt{3}s^2$
6) $\tilde{w}(t)$
7) $\int_a^bf(x)dx$ | \int_0^asinxdx
f(x,t)=t\cdot x
v=D\int idt
lim_{N\rightarrow+\infty}h_N=0
\frac{3}{2}\sqrt{3}s^2
\tilde{w}(t)
\int_a^bf(x)dx | [
{
"order": 1,
"latex": "\\int_0^asinxdx",
"bbox": [
94,
44,
546,
272
]
},
{
"order": 2,
"latex": "f(x,t)=t\\cdot x",
"bbox": [
94,
321,
526,
454
]
},
{
"order": 3,
"latex": "v=D\\int idt",
"bbox": [
94,
5... | |
097533 | human | handwriting | stack | photo | lines | 5 | 1,000 | 1,150 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{\partial L}{\partial q}=0$
$\frac{\partial}{\partial c}P_c^n(c)$
$\frac{\frac{\sqrt{84}}{8}-206}{\frac{(6\cdot\sqrt{3})}{7}}$
$\int xcosxdx$
$e^X=\sum_{k=0}^{\infty}\frac{1}{k!}X^k$ | \frac{\partial L}{\partial q}=0
\frac{\partial}{\partial c}P_c^n(c)
\frac{\frac{\sqrt{84}}{8}-206}{\frac{(6\cdot\sqrt{3})}{7}}
\int xcosxdx
e^X=\sum_{k=0}^{\infty}\frac{1}{k!}X^k | [
{
"order": 1,
"latex": "\\frac{\\partial L}{\\partial q}=0",
"bbox": [
48,
50,
207,
150
]
},
{
"order": 2,
"latex": "\\frac{\\partial}{\\partial c}P_c^n(c)",
"bbox": [
48,
183,
438,
343
]
},
{
"order": 3,
"latex": "\\fra... | |
027875 | human | handwriting | stack | photo | white | 6 | 1,000 | 1,224 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $([A,B]^T[A,B])^{-1}$
$k_1^{k_2^{k_6^{-^{-^{-}}}}}$
$\alpha=-\frac{log\frac{\Upsilon_{\varsigma_0}}{\Upsilon_{\varsigma_2}}}{log\frac{\varsigma_0}{\varsigma_2}}$
$\sum_{n=1}^{\infty}\frac{s_n}{n}$
$\frac{P_A}{1-P_A}=e^{v_A}$
$\sqrt[\infty]{\infty!}$ | ([A,B]^T[A,B])^{-1}
k_1^{k_2^{k_6^{-^{-^{-}}}}}
\alpha=-\frac{log\frac{\Upsilon_{\varsigma_0}}{\Upsilon_{\varsigma_2}}}{log\frac{\varsigma_0}{\varsigma_2}}
\sum_{n=1}^{\infty}\frac{s_n}{n}
\frac{P_A}{1-P_A}=e^{v_A}
\sqrt[\infty]{\infty!} | [
{
"order": 1,
"latex": "([A,B]^T[A,B])^{-1}",
"bbox": [
48,
48,
516,
139
]
},
{
"order": 2,
"latex": "k_1^{k_2^{k_6^{-^{-^{-}}}}}",
"bbox": [
48,
181,
455,
403
]
},
{
"order": 3,
"latex": "\\alpha=-\\frac{log\\frac{\\Ups... | |
036397 | human | handwriting | numbered | photo | white | 4 | 1,000 | 638 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $q=\frac{\partial\psi}{\partial n}$
2) $2\lfloor log_2(x)\rfloor+1$
3) $10^{20}<|G|<10^{130}$
4) $R=\frac{D_xln(D_e/D_i)}{\lambda}$ | q=\frac{\partial\psi}{\partial n}
2\lfloor log_2(x)\rfloor+1
10^{20}<|G|<10^{130}
R=\frac{D_xln(D_e/D_i)}{\lambda} | [
{
"order": 1,
"latex": "q=\\frac{\\partial\\psi}{\\partial n}",
"bbox": [
94,
50,
339,
207
]
},
{
"order": 2,
"latex": "2\\lfloor log_2(x)\\rfloor+1",
"bbox": [
94,
253,
466,
350
]
},
{
"order": 3,
"latex": "10^{20}<|G|<... | |
098744 | human | handwriting | numbered | photo | white | 5 | 1,000 | 846 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\frac{l_x}{l_i}=\frac{1}{\sqrt{1-\frac{t^2}{j^2}}}$
2) $[\hat{I}_{+},\hat{U}_{+}]=\hat{V}_{+}$
3) $\sqrt{\frac{\sum{D_j}^2}{w}}$
4) $\tilde{y}$
5) $\hat{m}_{+}$ | \frac{l_x}{l_i}=\frac{1}{\sqrt{1-\frac{t^2}{j^2}}}
[\hat{I}_{+},\hat{U}_{+}]=\hat{V}_{+}
\sqrt{\frac{\sum{D_j}^2}{w}}
\tilde{y}
\hat{m}_{+} | [
{
"order": 1,
"latex": "\\frac{l_x}{l_i}=\\frac{1}{\\sqrt{1-\\frac{t^2}{j^2}}}",
"bbox": [
94,
50,
225,
145
]
},
{
"order": 2,
"latex": "[\\hat{I}_{+},\\hat{U}_{+}]=\\hat{V}_{+}",
"bbox": [
94,
185,
442,
271
]
},
{
"order": ... | |
142934 | human | handwriting | grid | photo | white | 7 | 1,000 | 547 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\epsilon=100\frac{\theta-sin\theta}{sin\theta}$
$\begin{bmatrix}-5&7\\3&-4\end{bmatrix}$
$\underline{\varphi\vee\psi}$
$\sqrt{x^2+y^2}-L=0$
$e_3=\begin{pmatrix}1&0\\0&-1\end{pmatrix}$
$g(X)=1$
$C_R=\sqrt{\frac{h}{H}}$ | \epsilon=100\frac{\theta-sin\theta}{sin\theta}
\begin{bmatrix}-5&7\\3&-4\end{bmatrix}
\underline{\varphi\vee\psi}
\sqrt{x^2+y^2}-L=0
e_3=\begin{pmatrix}1&0\\0&-1\end{pmatrix}
g(X)=1
C_R=\sqrt{\frac{h}{H}} | [
{
"order": 1,
"latex": "\\epsilon=100\\frac{\\theta-sin\\theta}{sin\\theta}",
"bbox": [
48,
51,
274,
106
]
},
{
"order": 2,
"latex": "\\begin{bmatrix}-5&7\\\\3&-4\\end{bmatrix}",
"bbox": [
369,
52,
599,
165
]
},
{
"order": 3... | |
110536 | human | handwriting | twocol | photo | white | 8 | 1,000 | 853 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\int_E|f|<\epsilon$
$\int_{V_1}^{V_2}PdV$
$y(\underline{n})$
$\sqrt{rs}$
$\sqrt{(k+\frac{4}{3}u)/p}$
$\frac{\partial W}{\partial I_1}=C_1$
$n_{max}=\sqrt[3]{N}$
$-\int\frac{du}{u}$ | \int_E|f|<\epsilon
\int_{V_1}^{V_2}PdV
y(\underline{n})
\sqrt{rs}
\sqrt{(k+\frac{4}{3}u)/p}
\frac{\partial W}{\partial I_1}=C_1
n_{max}=\sqrt[3]{N}
-\int\frac{du}{u} | [
{
"order": 1,
"latex": "\\int_E|f|<\\epsilon",
"bbox": [
48,
46,
331,
200
]
},
{
"order": 2,
"latex": "\\int_{V_1}^{V_2}PdV",
"bbox": [
48,
244,
316,
391
]
},
{
"order": 3,
"latex": "y(\\underline{n})",
"bbox": [
... | |
055647 | human | handwriting | stack | photo | lines | 6 | 1,000 | 895 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{(287\cdot\sqrt{207})^8}{(122+155)}$
$H=-\frac{\partial S}{\partial t}$
$i=C\frac{du}{dt}$
$\epsilon_c<\epsilon_3<\epsilon_1<\epsilon_t$
$d((M,\varphi),(N,\psi))$
$\frac{2}{9}-\frac{1}{15}\sqrt{15}$ | \frac{(287\cdot\sqrt{207})^8}{(122+155)}
H=-\frac{\partial S}{\partial t}
i=C\frac{du}{dt}
\epsilon_c<\epsilon_3<\epsilon_1<\epsilon_t
d((M,\varphi),(N,\psi))
\frac{2}{9}-\frac{1}{15}\sqrt{15} | [
{
"order": 1,
"latex": "\\frac{(287\\cdot\\sqrt{207})^8}{(122+155)}",
"bbox": [
48,
50,
373,
262
]
},
{
"order": 2,
"latex": "H=-\\frac{\\partial S}{\\partial t}",
"bbox": [
48,
301,
237,
358
]
},
{
"order": 3,
"latex": ... | |
181832 | human | handwriting | twocol | photo | white | 8 | 1,000 | 835 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\prod_{i=1}^n(n+i)/2n$
$a=\sqrt{2\varphi^{-1}}$
$\sum_{i=1}^l\binom{2m}{i}\leq N-K+1$
$\tilde{O}(log^4q)$
$5^{5^{5^{5^{5^5}}}}-7$
$R=\frac{Z_2-Z_1}{Z_2+Z_1}$
$n=(n_1,n_2,n_3)$
$A=B=C$ | \prod_{i=1}^n(n+i)/2n
a=\sqrt{2\varphi^{-1}}
\sum_{i=1}^l\binom{2m}{i}\leq N-K+1
\tilde{O}(log^4q)
5^{5^{5^{5^{5^5}}}}-7
R=\frac{Z_2-Z_1}{Z_2+Z_1}
n=(n_1,n_2,n_3)
A=B=C | [
{
"order": 1,
"latex": "\\prod_{i=1}^n(n+i)/2n",
"bbox": [
48,
50,
367,
189
]
},
{
"order": 2,
"latex": "a=\\sqrt{2\\varphi^{-1}}",
"bbox": [
48,
225,
436,
345
]
},
{
"order": 3,
"latex": "\\sum_{i=1}^l\\binom{2m}{i}\\le... | |
126858 | human | handwriting | grid | photo | white | 7 | 1,000 | 526 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $1+z=\frac{\gamma_s(1-v_{s||})}{\gamma_r(1-v_{r||})}$
$s\in\prod_{i=1}^l\mathbb{Z}^k$
$w=\frac{\sqrt{8t+1}-1}{2}$
$C_{abs}$
$((\frac{\sqrt{141}}{5})^9)^{\frac{6}{159}/10}$
$\tilde{C}$
$f(0,...)=f(0,...)$ | 1+z=\frac{\gamma_s(1-v_{s||})}{\gamma_r(1-v_{r||})}
s\in\prod_{i=1}^l\mathbb{Z}^k
w=\frac{\sqrt{8t+1}-1}{2}
C_{abs}
((\frac{\sqrt{141}}{5})^9)^{\frac{6}{159}/10}
\tilde{C}
f(0,...)=f(0,...) | [
{
"order": 1,
"latex": "1+z=\\frac{\\gamma_s(1-v_{s||})}{\\gamma_r(1-v_{r||})}",
"bbox": [
48,
44,
266,
114
]
},
{
"order": 2,
"latex": "s\\in\\prod_{i=1}^l\\mathbb{Z}^k",
"bbox": [
369,
49,
630,
165
]
},
{
"order": 3,
"... | |
160923 | human | handwriting | grid | photo | grid | 9 | 1,000 | 555 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\lambda_B=\frac{e^2}{4\pi\epsilon_0\epsilon_rk_BT}$
$perm^{(s_1,s_2,...,s_n)}(A)$
$\hat{w}_i^{\prime}$
$3^{3^{3^{3^{46}}}}$
$\int_B\psi dx=1$
$z_2=cos\eta e^{i\varphi/2}$
$w=(\langle\overline{M}\rangle,10^k)$
$\sqrt{x^2}=\sqrt{4}$
$h_{\overline{z}}=\mu(z)h_z$ | \lambda_B=\frac{e^2}{4\pi\epsilon_0\epsilon_rk_BT}
perm^{(s_1,s_2,...,s_n)}(A)
\hat{w}_i^{\prime}
3^{3^{3^{3^{46}}}}
\int_B\psi dx=1
z_2=cos\eta e^{i\varphi/2}
w=(\langle\overline{M}\rangle,10^k)
\sqrt{x^2}=\sqrt{4}
h_{\overline{z}}=\mu(z)h_z | [
{
"order": 1,
"latex": "\\lambda_B=\\frac{e^2}{4\\pi\\epsilon_0\\epsilon_rk_BT}",
"bbox": [
48,
44,
309,
144
]
},
{
"order": 2,
"latex": "perm^{(s_1,s_2,...,s_n)}(A)",
"bbox": [
369,
49,
630,
108
]
},
{
"order": 3,
"late... | |
176552 | human | handwriting | numbered | photo | lines | 6 | 1,000 | 1,239 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $E=\frac{fa^4}{\sqrt{1\cdot\frac{v^4}{a^4}}}$
2) $lim_{x\rightarrow3}\frac{\sqrt{x-3}}{x^2-9}$
3) $R_0=\frac{\beta\Lambda}{\mu(\mu+\gamma)}$
4) $W=\frac{1}{\sqrt{2}}\begin{bmatrix}1&1\\1&-1\end{bmatrix}$
5) $r\begin{Bmatrix}3\\3,4\end{Bmatrix}$
6) $(\frac{5}{4}/359)/\sqrt{8}^{146}$ | E=\frac{fa^4}{\sqrt{1\cdot\frac{v^4}{a^4}}}
lim_{x\rightarrow3}\frac{\sqrt{x-3}}{x^2-9}
R_0=\frac{\beta\Lambda}{\mu(\mu+\gamma)}
W=\frac{1}{\sqrt{2}}\begin{bmatrix}1&1\\1&-1\end{bmatrix}
r\begin{Bmatrix}3\\3,4\end{Bmatrix}
(\frac{5}{4}/359)/\sqrt{8}^{146} | [
{
"order": 1,
"latex": "E=\\frac{fa^4}{\\sqrt{1\\cdot\\frac{v^4}{a^4}}}",
"bbox": [
94,
44,
366,
217
]
},
{
"order": 2,
"latex": "lim_{x\\rightarrow3}\\frac{\\sqrt{x-3}}{x^2-9}",
"bbox": [
94,
249,
450,
392
]
},
{
"order": 3... | |
066878 | human | handwriting | stack | photo | white | 6 | 1,000 | 1,366 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{1}{|a|}\cdot tri(\frac{\xi}{a})$
$x\notin C$
$R_E=c/\sqrt{4\pi G\rho}$
$\sqrt{-3}$
$2^{O(\sqrt{k})}n^{O(1)}$
$\{i,j\}\notin E$ | \frac{1}{|a|}\cdot tri(\frac{\xi}{a})
x\notin C
R_E=c/\sqrt{4\pi G\rho}
\sqrt{-3}
2^{O(\sqrt{k})}n^{O(1)}
\{i,j\}\notin E | [
{
"order": 1,
"latex": "\\frac{1}{|a|}\\cdot tri(\\frac{\\xi}{a})",
"bbox": [
48,
44,
341,
184
]
},
{
"order": 2,
"latex": "x\\notin C",
"bbox": [
48,
223,
429,
432
]
},
{
"order": 3,
"latex": "R_E=c/\\sqrt{4\\pi G\\rho}... | |
002977 | human | handwriting | grid | photo | white | 7 | 1,000 | 672 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $9^{144}+5^9$
$368+8-\frac{483}{\sqrt{206}}$
$\prod_{j\neq i}(x_i-x_j)$
$\begin{bmatrix}1&k\\0&1\end{bmatrix}$
$u=\frac{t+s}{2}$
$\frac{310-9}{\frac{2}{6}+4}$
$\frac{\partial C}{\partial\sigma}$ | 9^{144}+5^9
368+8-\frac{483}{\sqrt{206}}
\prod_{j\neq i}(x_i-x_j)
\begin{bmatrix}1&k\\0&1\end{bmatrix}
u=\frac{t+s}{2}
\frac{310-9}{\frac{2}{6}+4}
\frac{\partial C}{\partial\sigma} | [
{
"order": 1,
"latex": "9^{144}+5^9",
"bbox": [
48,
51,
309,
168
]
},
{
"order": 2,
"latex": "368+8-\\frac{483}{\\sqrt{206}}",
"bbox": [
369,
52,
587,
148
]
},
{
"order": 3,
"latex": "\\prod_{j\\neq i}(x_i-x_j)",
"bb... | |
191855 | human | handwriting | numbered | photo | lines | 7 | 1,000 | 1,189 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\tilde{\Omega}$
2) $A(G)(x,y)$
3) $r_i=\frac{1}{C(i)}$
4) $\int_{t1}^{t2}Ldt$
5) $\psi=\binom{\chi}{\eta}$
6) $T=0.20P_{pre}d$
7) $1/\epsilon_0=10^{-7}c_0^2$ | \tilde{\Omega}
A(G)(x,y)
r_i=\frac{1}{C(i)}
\int_{t1}^{t2}Ldt
\psi=\binom{\chi}{\eta}
T=0.20P_{pre}d
1/\epsilon_0=10^{-7}c_0^2 | [
{
"order": 1,
"latex": "\\tilde{\\Omega}",
"bbox": [
94,
48,
270,
235
]
},
{
"order": 2,
"latex": "A(G)(x,y)",
"bbox": [
94,
258,
426,
341
]
},
{
"order": 3,
"latex": "r_i=\\frac{1}{C(i)}",
"bbox": [
94,
... | |
123287 | human | handwriting | numbered | photo | lines | 5 | 1,000 | 709 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $a_1^{a_9^{-^{-^{a_y}}}}$
2) $D^{(r)}X^n=\binom{n}{r}X^{n-r}$
3) $c>a>b$
4) $A=\tilde{A}^T\tilde{A}$
5) $a=\frac{3t}{\sqrt{10}}+3k$ | a_1^{a_9^{-^{-^{a_y}}}}
D^{(r)}X^n=\binom{n}{r}X^{n-r}
c>a>b
A=\tilde{A}^T\tilde{A}
a=\frac{3t}{\sqrt{10}}+3k | [
{
"order": 1,
"latex": "a_1^{a_9^{-^{-^{a_y}}}}",
"bbox": [
94,
50,
232,
150
]
},
{
"order": 2,
"latex": "D^{(r)}X^n=\\binom{n}{r}X^{n-r}",
"bbox": [
94,
179,
295,
231
]
},
{
"order": 3,
"latex": "c>a>b",
"bbox": [
... | |
174300 | human | handwriting | grid | photo | grid | 9 | 1,000 | 545 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{d((Ax)\circ B)}{dx}$
$\frac{1}{\nu+2}$
$2^k\leq s(F)<2^{k+1}$
$q=-k\frac{\partial u}{\partial x}$
$t=\frac{q_3v}{\sqrt{1\cdot\frac{v^2}{c^2}}}$
$AB$
$|f|=exp(-v(f))$
$T(O_r^{*}),O_n$
${26^{156}}^{\frac{2^{133}}{203}}$ | \frac{d((Ax)\circ B)}{dx}
\frac{1}{\nu+2}
2^k\leq s(F)<2^{k+1}
q=-k\frac{\partial u}{\partial x}
t=\frac{q_3v}{\sqrt{1\cdot\frac{v^2}{c^2}}}
AB
|f|=exp(-v(f))
T(O_r^{*}),O_n
{26^{156}}^{\frac{2^{133}}{203}} | [
{
"order": 1,
"latex": "\\frac{d((Ax)\\circ B)}{dx}",
"bbox": [
48,
48,
309,
192
]
},
{
"order": 2,
"latex": "\\frac{1}{\\nu+2}",
"bbox": [
369,
50,
630,
186
]
},
{
"order": 3,
"latex": "2^k\\leq s(F)<2^{k+1}",
"bbox... | |
097959 | human | handwriting | twocol | photo | white | 11 | 1,000 | 1,031 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $T1=\frac{a_1}{\sum_{h=1}^Ha_h}$
$u\notin V^{\prime},W^{\prime}$
$lim_{n\rightarrow\infty}\frac{N(n,S)}{n}=0$
$\tilde{d}$
$\langle M_C\rangle$
$\frac{\frac{1}{4}}{138+4}$
$T=\frac{\partial U}{\partial S}$
$\int\sigma_xdA=0$
$(\frac{2}{1}+8)^{\frac{8}{\sqrt{9}}}$
$|\frac{\partial S}{\partial y}|\ll1$
$10-5^{\frac{1}{99}... | T1=\frac{a_1}{\sum_{h=1}^Ha_h}
u\notin V^{\prime},W^{\prime}
lim_{n\rightarrow\infty}\frac{N(n,S)}{n}=0
\tilde{d}
\langle M_C\rangle
\frac{\frac{1}{4}}{138+4}
T=\frac{\partial U}{\partial S}
\int\sigma_xdA=0
(\frac{2}{1}+8)^{\frac{8}{\sqrt{9}}}
|\frac{\partial S}{\partial y}|\ll1
10-5^{\frac{1}{99}} | [
{
"order": 1,
"latex": "T1=\\frac{a_1}{\\sum_{h=1}^Ha_h}",
"bbox": [
48,
50,
446,
203
]
},
{
"order": 2,
"latex": "u\\notin V^{\\prime},W^{\\prime}",
"bbox": [
48,
234,
470,
371
]
},
{
"order": 3,
"latex": "lim_{n\\right... | |
150617 | human | handwriting | stack | photo | white | 5 | 1,000 | 816 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{47+1}{100+2}=0.47$
$\binom{7}{2}=6\times\frac{7}{2}=21$
$\frac{2}{7}\sqrt{10-\sqrt{2}}$
$A=\frac{\alpha}{360}\pi r^2$
$E[F]<1$ | \frac{47+1}{100+2}=0.47
\binom{7}{2}=6\times\frac{7}{2}=21
\frac{2}{7}\sqrt{10-\sqrt{2}}
A=\frac{\alpha}{360}\pi r^2
E[F]<1 | [
{
"order": 1,
"latex": "\\frac{47+1}{100+2}=0.47",
"bbox": [
48,
50,
314,
148
]
},
{
"order": 2,
"latex": "\\binom{7}{2}=6\\times\\frac{7}{2}=21",
"bbox": [
48,
185,
563,
353
]
},
{
"order": 3,
"latex": "\\frac{2}{7}\\sq... | |
086996 | human | handwriting | numbered | photo | white | 6 | 1,000 | 1,143 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $-\sqrt{\frac{8}{35}}$
2) $\frac{V_1}{V_2}$
3) $\int sin(cos(x))dx$
4) $R(r,s)\leq\binom{r+s-2}{r-1}$
5) $\binom{n}{k}$
6) $A+\overline{D}$ | -\sqrt{\frac{8}{35}}
\frac{V_1}{V_2}
\int sin(cos(x))dx
R(r,s)\leq\binom{r+s-2}{r-1}
\binom{n}{k}
A+\overline{D} | [
{
"order": 1,
"latex": "-\\sqrt{\\frac{8}{35}}",
"bbox": [
94,
49,
470,
279
]
},
{
"order": 2,
"latex": "\\frac{V_1}{V_2}",
"bbox": [
94,
319,
159,
450
]
},
{
"order": 3,
"latex": "\\int sin(cos(x))dx",
"bbox": [
... | |
015153 | human | handwriting | grid | photo | grid | 7 | 1,000 | 573 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{\frac{(8\cdot\sqrt{303})}{24}}{6^{374}\cdot7}$
$\frac{b}{a^2+b^2}$
$O(\frac{1}{t_0})$
$Q=-1+(\frac{K}{Y_0})^{\nu}$
$s\begin{Bmatrix}3\\3,4,3\end{Bmatrix}$
$\hat{g}(f)$
$y=f(x)=\frac{a+bx}{c+dx}$ | \frac{\frac{(8\cdot\sqrt{303})}{24}}{6^{374}\cdot7}
\frac{b}{a^2+b^2}
O(\frac{1}{t_0})
Q=-1+(\frac{K}{Y_0})^{\nu}
s\begin{Bmatrix}3\\3,4,3\end{Bmatrix}
\hat{g}(f)
y=f(x)=\frac{a+bx}{c+dx} | [
{
"order": 1,
"latex": "\\frac{\\frac{(8\\cdot\\sqrt{303})}{24}}{6^{374}\\cdot7}",
"bbox": [
48,
48,
272,
234
]
},
{
"order": 2,
"latex": "\\frac{b}{a^2+b^2}",
"bbox": [
369,
47,
465,
161
]
},
{
"order": 3,
"latex": "O(\... | |
020344 | human | handwriting | numbered | photo | white | 5 | 1,000 | 1,032 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $Q=\frac{4\pi sin(\theta)}{\lambda}$
2) $a<x<b$
3) $(\frac{1}{2})^{\frac{32}{\sqrt{489}}}$
4) $\frac{(\frac{493}{8})^{470}}{\frac{31}{4}}$
5) $\begin{pmatrix}0&F\\-F&0\end{pmatrix}$ | Q=\frac{4\pi sin(\theta)}{\lambda}
a<x<b
(\frac{1}{2})^{\frac{32}{\sqrt{489}}}
\frac{(\frac{493}{8})^{470}}{\frac{31}{4}}
\begin{pmatrix}0&F\\-F&0\end{pmatrix} | [
{
"order": 1,
"latex": "Q=\\frac{4\\pi sin(\\theta)}{\\lambda}",
"bbox": [
94,
44,
424,
142
]
},
{
"order": 2,
"latex": "a<x<b",
"bbox": [
94,
192,
445,
274
]
},
{
"order": 3,
"latex": "(\\frac{1}{2})^{\\frac{32}{\\sqrt{... | |
115462 | human | handwriting | numbered | photo | white | 4 | 1,000 | 810 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $G(t)=\int_0^tg(s)ds$
2) $((3\cdot6)+\frac{3}{2})$
3) $S=\int wdx$
4) $m(A)=\int_AXdn$ | G(t)=\int_0^tg(s)ds
((3\cdot6)+\frac{3}{2})
S=\int wdx
m(A)=\int_AXdn | [
{
"order": 1,
"latex": "G(t)=\\int_0^tg(s)ds",
"bbox": [
94,
45,
818,
269
]
},
{
"order": 2,
"latex": "((3\\cdot6)+\\frac{3}{2})",
"bbox": [
94,
298,
431,
417
]
},
{
"order": 3,
"latex": "S=\\int wdx",
"bbox": [
... | |
103056 | human | handwriting | numbered | photo | lines | 6 | 1,000 | 933 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $r$
2) $\begin{bmatrix}x\\\frac{1}{x}\end{bmatrix}$
3) $\vec{s}_i\in R^3,|\vec{s}_i|=1(1)$
4) $\int vdp$
5) $\rho_{t_0}^{t_1}(x_0,n_0)$
6) $q_{y=0}=1-\hat{y}$ | r
\begin{bmatrix}x\\\frac{1}{x}\end{bmatrix}
\vec{s}_i\in R^3,|\vec{s}_i|=1(1)
\int vdp
\rho_{t_0}^{t_1}(x_0,n_0)
q_{y=0}=1-\hat{y} | [
{
"order": 1,
"latex": "r",
"bbox": [
94,
44,
142,
106
]
},
{
"order": 2,
"latex": "\\begin{bmatrix}x\\\\\\frac{1}{x}\\end{bmatrix}",
"bbox": [
94,
155,
259,
281
]
},
{
"order": 3,
"latex": "\\vec{s}_i\\in R^3,|\\vec{s}_... | |
198302 | human | handwriting | stack | photo | lines | 5 | 1,000 | 978 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $d_e=\frac{d_r}{\sqrt{\frac{d_r}{d_m}}}$
$\delta_{pq}$
$(\frac{9^7}{6}+\frac{92+\sqrt{3}}{1})$
$\frac{73+1}{{7^4}^{280}}$
$\sigma=(x_n^2)_{n=0,...,M-1}$ | d_e=\frac{d_r}{\sqrt{\frac{d_r}{d_m}}}
\delta_{pq}
(\frac{9^7}{6}+\frac{92+\sqrt{3}}{1})
\frac{73+1}{{7^4}^{280}}
\sigma=(x_n^2)_{n=0,...,M-1} | [
{
"order": 1,
"latex": "d_e=\\frac{d_r}{\\sqrt{\\frac{d_r}{d_m}}}",
"bbox": [
48,
51,
189,
130
]
},
{
"order": 2,
"latex": "\\delta_{pq}",
"bbox": [
48,
159,
311,
385
]
},
{
"order": 3,
"latex": "(\\frac{9^7}{6}+\\frac{9... | |
189195 | human | handwriting | grid | photo | grid | 7 | 1,000 | 673 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $f=\tilde{f}i$
$(3-364)^{\frac{\sqrt{14}^9}{325}}$
$\frac{d^2F_0}{dk^2}+\frac{1}{k}\frac{dF_0}{dk}$
$z=\frac{h}{\sqrt[8]{\cdot\frac{u_1}{5}}}$
$k\propto\frac{c}{\sigma}v$
$w_i=\frac{\rho_i}{\rho}$
$\frac{d(v)}{d(w)+d(v)}$ | f=\tilde{f}i
(3-364)^{\frac{\sqrt{14}^9}{325}}
\frac{d^2F_0}{dk^2}+\frac{1}{k}\frac{dF_0}{dk}
z=\frac{h}{\sqrt[8]{\cdot\frac{u_1}{5}}}
k\propto\frac{c}{\sigma}v
w_i=\frac{\rho_i}{\rho}
\frac{d(v)}{d(w)+d(v)} | [
{
"order": 1,
"latex": "f=\\tilde{f}i",
"bbox": [
48,
49,
309,
212
]
},
{
"order": 2,
"latex": "(3-364)^{\\frac{\\sqrt{14}^9}{325}}",
"bbox": [
369,
50,
630,
217
]
},
{
"order": 3,
"latex": "\\frac{d^2F_0}{dk^2}+\\frac{1... | |
057706 | human | handwriting | grid | photo | grid | 7 | 1,000 | 634 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $u=\prod_{i=1}^{k/2}p_i$
$T_0=2\pi\sqrt{\frac{l}{g}}$
${{6^6}^5}^{{250^6}^1}$
$\hat{e}_j$
$\tau_{true}=\frac{d_{spacing}}{c}$
$\hat{\zeta}$
$\int Ldt$ | u=\prod_{i=1}^{k/2}p_i
T_0=2\pi\sqrt{\frac{l}{g}}
{{6^6}^5}^{{250^6}^1}
\hat{e}_j
\tau_{true}=\frac{d_{spacing}}{c}
\hat{\zeta}
\int Ldt | [
{
"order": 1,
"latex": "u=\\prod_{i=1}^{k/2}p_i",
"bbox": [
48,
47,
309,
193
]
},
{
"order": 2,
"latex": "T_0=2\\pi\\sqrt{\\frac{l}{g}}",
"bbox": [
369,
52,
524,
126
]
},
{
"order": 3,
"latex": "{{6^6}^5}^{{250^6}^1}",
... | |
094728 | human | handwriting | numbered | photo | white | 7 | 1,000 | 1,274 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\overline{lnx}$
2) $(\sqrt{\frac{1}{3}})^{n^2}$
3) $\tilde{\psi}(t)$
4) $F=\int\Pi(x)dA$
5) $\frac{e^{hk}p^k(1-p)^{n-k}}{1-p+pe^h}$
6) $|m|>b/a$
7) $\frac{\partial r_i}{\partial\beta_j}$ | \overline{lnx}
(\sqrt{\frac{1}{3}})^{n^2}
\tilde{\psi}(t)
F=\int\Pi(x)dA
\frac{e^{hk}p^k(1-p)^{n-k}}{1-p+pe^h}
|m|>b/a
\frac{\partial r_i}{\partial\beta_j} | [
{
"order": 1,
"latex": "\\overline{lnx}",
"bbox": [
94,
46,
452,
278
]
},
{
"order": 2,
"latex": "(\\sqrt{\\frac{1}{3}})^{n^2}",
"bbox": [
94,
319,
282,
445
]
},
{
"order": 3,
"latex": "\\tilde{\\psi}(t)",
"bbox": [
... | |
178782 | human | handwriting | numbered | photo | lines | 4 | 1,000 | 681 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $10^6/\frac{\frac{180}{6}}{194}$
2) $x\notin C$
3) $\prod{A_i}^{\prime}$
4) $\binom{n}{k}$ | 10^6/\frac{\frac{180}{6}}{194}
x\notin C
\prod{A_i}^{\prime}
\binom{n}{k} | [
{
"order": 1,
"latex": "10^6/\\frac{\\frac{180}{6}}{194}",
"bbox": [
94,
46,
393,
192
]
},
{
"order": 2,
"latex": "x\\notin C",
"bbox": [
94,
224,
253,
284
]
},
{
"order": 3,
"latex": "\\prod{A_i}^{\\prime}",
"bbox":... | |
159646 | human | handwriting | numbered | photo | lines | 5 | 1,000 | 727 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\hat{h}_L$
2) $\frac{dP}{dw}$
3) $\overline{-s}$
4) $m_{rwl}=\frac{m_0}{\sqrt{7\cdot\frac{g^8}{c^8}}}$
5) $R=\frac{1}{2}tcsc\frac{\pi}{70}$ | \hat{h}_L
\frac{dP}{dw}
\overline{-s}
m_{rwl}=\frac{m_0}{\sqrt{7\cdot\frac{g^8}{c^8}}}
R=\frac{1}{2}tcsc\frac{\pi}{70} | [
{
"order": 1,
"latex": "\\hat{h}_L",
"bbox": [
94,
47,
165,
112
]
},
{
"order": 2,
"latex": "\\frac{dP}{dw}",
"bbox": [
94,
145,
236,
308
]
},
{
"order": 3,
"latex": "\\overline{-s}",
"bbox": [
94,
354,
... | |
139392 | human | handwriting | stack | photo | lines | 6 | 1,000 | 945 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $m=l+\bigoplus_{i\leq-2}g(i)$
$J=\int f(t,x,y)dt$
$(261+169+\frac{3}{24}+141)$
$v_e[OH^{-}]_0/v_e^{\prime}$
$\begin{bmatrix}w^1\\\vdots\\w^k\end{bmatrix}$
$H_2:G_2\rightarrow\{0,1\}^n$ | m=l+\bigoplus_{i\leq-2}g(i)
J=\int f(t,x,y)dt
(261+169+\frac{3}{24}+141)
v_e[OH^{-}]_0/v_e^{\prime}
\begin{bmatrix}w^1\\\vdots\\w^k\end{bmatrix}
H_2:G_2\rightarrow\{0,1\}^n | [
{
"order": 1,
"latex": "m=l+\\bigoplus_{i\\leq-2}g(i)",
"bbox": [
48,
45,
434,
164
]
},
{
"order": 2,
"latex": "J=\\int f(t,x,y)dt",
"bbox": [
48,
219,
434,
313
]
},
{
"order": 3,
"latex": "(261+169+\\frac{3}{24}+141)",
... | |
074841 | human | handwriting | twocol | photo | white | 10 | 1,000 | 831 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $C=\frac{\partial P}{\partial\rho}$
$w^{+\frac{(V+M)^2}{2{(s_V)}^2}}$
$C=\overline{A}$
$\hat{v}$
$\overline{x}$
$\int_UL(Dw)dx$
$\hat{y}_d$
$\begin{pmatrix}1&a\\0&1\end{pmatrix}$
$\overline{V^{\prime}L}$
$\overline{X}_0$ | C=\frac{\partial P}{\partial\rho}
w^{+\frac{(V+M)^2}{2{(s_V)}^2}}
C=\overline{A}
\hat{v}
\overline{x}
\int_UL(Dw)dx
\hat{y}_d
\begin{pmatrix}1&a\\0&1\end{pmatrix}
\overline{V^{\prime}L}
\overline{X}_0 | [
{
"order": 1,
"latex": "C=\\frac{\\partial P}{\\partial\\rho}",
"bbox": [
48,
48,
304,
176
]
},
{
"order": 2,
"latex": "w^{+\\frac{(V+M)^2}{2{(s_V)}^2}}",
"bbox": [
48,
203,
470,
390
]
},
{
"order": 3,
"latex": "C=\\over... | |
079843 | human | handwriting | stack | photo | white | 6 | 1,000 | 1,105 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $|\frac{a_{n+1}}{a_n}|$
$D=\pm\prod_{j<k}(a_j-a_k)$
$\frac{\partial}{\partial c}\frac{\partial}{\partial z}P_c^p(z_0)$
$\frac{x^2}{2}=\frac{\sqrt{5}}{2}$
$\mathbb{B}$
$\overline{N}(f)$ | |\frac{a_{n+1}}{a_n}|
D=\pm\prod_{j<k}(a_j-a_k)
\frac{\partial}{\partial c}\frac{\partial}{\partial z}P_c^p(z_0)
\frac{x^2}{2}=\frac{\sqrt{5}}{2}
\mathbb{B}
\overline{N}(f) | [
{
"order": 1,
"latex": "|\\frac{a_{n+1}}{a_n}|",
"bbox": [
48,
45,
287,
271
]
},
{
"order": 2,
"latex": "D=\\pm\\prod_{j<k}(a_j-a_k)",
"bbox": [
48,
309,
820,
523
]
},
{
"order": 3,
"latex": "\\frac{\\partial}{\\partial ... | |
080820 | human | handwriting | stack | photo | lines | 5 | 1,000 | 1,094 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $0\notin S$
$\hat{\beta}=(X^{\prime}X)^{-1}X^{\prime}y$
$\frac{8\pi g}{\sqrt{9-\frac{2g}{rh^2}}}$
$50^{50^{50^{50^{59}}}}$
$t=\frac{7}{\sqrt{7\cdot\frac{a^2}{r^2}}}\tau$ | 0\notin S
\hat{\beta}=(X^{\prime}X)^{-1}X^{\prime}y
\frac{8\pi g}{\sqrt{9-\frac{2g}{rh^2}}}
50^{50^{50^{50^{59}}}}
t=\frac{7}{\sqrt{7\cdot\frac{a^2}{r^2}}}\tau | [
{
"order": 1,
"latex": "0\\notin S",
"bbox": [
48,
48,
191,
129
]
},
{
"order": 2,
"latex": "\\hat{\\beta}=(X^{\\prime}X)^{-1}X^{\\prime}y",
"bbox": [
48,
167,
659,
399
]
},
{
"order": 3,
"latex": "\\frac{8\\pi g}{\\sqrt... | |
053637 | human | handwriting | twocol | photo | white | 11 | 1,000 | 1,164 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $(402+91)^{\frac{(25+3)}{2}}$
$(\sqrt{10}\cdot3)\cdot\frac{375-26}{96}$
$\hat{y}=-37+5.1x$
$V_{\alpha+1}$
$RTI_{20}=\frac{h}{b}\times2924$
$\frac{(6/\sqrt{209})^6}{10^{169}}$
$m(x)=inf\frac{f^{\prime}(\xi)}{g^{\prime}(\xi)}$
$\binom{U_1}{U_2}$
$|x^{\rho}|=\sqrt{x}$
$N=1,2,3,...$
$q=\frac{z}{\sqrt{4\cdot\frac{e\cdot P}{... | (402+91)^{\frac{(25+3)}{2}}
(\sqrt{10}\cdot3)\cdot\frac{375-26}{96}
\hat{y}=-37+5.1x
V_{\alpha+1}
RTI_{20}=\frac{h}{b}\times2924
\frac{(6/\sqrt{209})^6}{10^{169}}
m(x)=inf\frac{f^{\prime}(\xi)}{g^{\prime}(\xi)}
\binom{U_1}{U_2}
|x^{\rho}|=\sqrt{x}
N=1,2,3,...
q=\frac{z}{\sqrt{4\cdot\frac{e\cdot P}{2P_m}}} | [
{
"order": 1,
"latex": "(402+91)^{\\frac{(25+3)}{2}}",
"bbox": [
48,
48,
198,
125
]
},
{
"order": 2,
"latex": "(\\sqrt{10}\\cdot3)\\cdot\\frac{375-26}{96}",
"bbox": [
48,
152,
362,
323
]
},
{
"order": 3,
"latex": "\\hat{... | |
058355 | human | handwriting | numbered | photo | lines | 5 | 1,000 | 896 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $wL/Y$
2) $\tau_1\circ_s\tau_2$
3) $F_0=-k_BTlnZ_0$
4) ${(\omega^{\zeta})}^8$
5) $\overline{v}=\frac{v-u}{2}$ | wL/Y
\tau_1\circ_s\tau_2
F_0=-k_BTlnZ_0
{(\omega^{\zeta})}^8
\overline{v}=\frac{v-u}{2} | [
{
"order": 1,
"latex": "wL/Y",
"bbox": [
94,
46,
505,
268
]
},
{
"order": 2,
"latex": "\\tau_1\\circ_s\\tau_2",
"bbox": [
94,
311,
305,
373
]
},
{
"order": 3,
"latex": "F_0=-k_BTlnZ_0",
"bbox": [
94,
411,... | |
157593 | human | handwriting | stack | photo | lines | 5 | 1,000 | 1,072 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $g_n<2\sqrt{p_n}+1$
$J_i=-\sum_{j=1}^3D_{ij}\frac{\partial\phi}{\partial x_j}$
$\hat{S}_N$
${(x^{\chi})}^9$
$u=\frac{mx}{\sqrt{1\cdot\frac{x^7}{c^7}}}$ | g_n<2\sqrt{p_n}+1
J_i=-\sum_{j=1}^3D_{ij}\frac{\partial\phi}{\partial x_j}
\hat{S}_N
{(x^{\chi})}^9
u=\frac{mx}{\sqrt{1\cdot\frac{x^7}{c^7}}} | [
{
"order": 1,
"latex": "g_n<2\\sqrt{p_n}+1",
"bbox": [
48,
52,
738,
286
]
},
{
"order": 2,
"latex": "J_i=-\\sum_{j=1}^3D_{ij}\\frac{\\partial\\phi}{\\partial x_j}",
"bbox": [
48,
329,
356,
452
]
},
{
"order": 3,
"latex":... | |
118152 | human | handwriting | numbered | photo | white | 5 | 1,000 | 1,059 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $ETX=\frac{1}{1-e_{pt}}$
2) $r=\sqrt{\frac{A}{\pi}}$
3) $u=\frac{mx}{\sqrt{1\cdot\frac{x^7}{c^7}}}$
4) $\frac{V_{out}}{V_{in}}=-\frac{R_f}{R_{in}}$
5) $\hat{w}$ | ETX=\frac{1}{1-e_{pt}}
r=\sqrt{\frac{A}{\pi}}
u=\frac{mx}{\sqrt{1\cdot\frac{x^7}{c^7}}}
\frac{V_{out}}{V_{in}}=-\frac{R_f}{R_{in}}
\hat{w} | [
{
"order": 1,
"latex": "ETX=\\frac{1}{1-e_{pt}}",
"bbox": [
94,
46,
477,
197
]
},
{
"order": 2,
"latex": "r=\\sqrt{\\frac{A}{\\pi}}",
"bbox": [
94,
225,
400,
406
]
},
{
"order": 3,
"latex": "u=\\frac{mx}{\\sqrt{1\\cdot\\... | |
191185 | human | handwriting | stack | photo | lines | 5 | 1,000 | 1,058 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{f_r}{f_y}=\frac{1}{\sqrt{1-\frac{i^5}{a^5}}}$
$\frac{\partial^2f}{\partial\sigma^2}<0$
$|2\rangle=\binom{0}{1}$
$\int_{x_s(t)+\epsilon}^{x_2}w_tdx\rightarrow0$
$\frac{e^{\frac{(u-q)^3}{9}}}{i\sqrt{9\iota}}$ | \frac{f_r}{f_y}=\frac{1}{\sqrt{1-\frac{i^5}{a^5}}}
\frac{\partial^2f}{\partial\sigma^2}<0
|2\rangle=\binom{0}{1}
\int_{x_s(t)+\epsilon}^{x_2}w_tdx\rightarrow0
\frac{e^{\frac{(u-q)^3}{9}}}{i\sqrt{9\iota}} | [
{
"order": 1,
"latex": "\\frac{f_r}{f_y}=\\frac{1}{\\sqrt{1-\\frac{i^5}{a^5}}}",
"bbox": [
48,
50,
400,
235
]
},
{
"order": 2,
"latex": "\\frac{\\partial^2f}{\\partial\\sigma^2}<0",
"bbox": [
48,
271,
348,
438
]
},
{
"order"... | |
079217 | human | handwriting | numbered | photo | white | 5 | 1,000 | 904 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $h_{B_1}(x)=|x|$
2) $t_0=\frac{1}{\sqrt{3}}$
3) $\int\sqrt{x^2+a^2}dx$
4) $\{4,5\}^{2^{2^{\aleph_4}}}$
5) $y^2=\sqrt{b^2-\frac{b^2x}{a^2}}$ | h_{B_1}(x)=|x|
t_0=\frac{1}{\sqrt{3}}
\int\sqrt{x^2+a^2}dx
\{4,5\}^{2^{2^{\aleph_4}}}
y^2=\sqrt{b^2-\frac{b^2x}{a^2}} | [
{
"order": 1,
"latex": "h_{B_1}(x)=|x|",
"bbox": [
94,
48,
351,
120
]
},
{
"order": 2,
"latex": "t_0=\\frac{1}{\\sqrt{3}}",
"bbox": [
94,
146,
401,
319
]
},
{
"order": 3,
"latex": "\\int\\sqrt{x^2+a^2}dx",
"bbox": [
... | |
018665 | human | handwriting | numbered | photo | lines | 4 | 1,000 | 968 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\vec{F}_E=q\vec{E}$
2) $\frac{\varphi(n)}{n}$
3) $\frac{e^{\cdot\frac{x^8}{8\sigma^8}}}{\sqrt{8\vartheta}\sigma}$
4) $\nabla\cdot E=\frac{\rho}{\epsilon_0}$ | \vec{F}_E=q\vec{E}
\frac{\varphi(n)}{n}
\frac{e^{\cdot\frac{x^8}{8\sigma^8}}}{\sqrt{8\vartheta}\sigma}
\nabla\cdot E=\frac{\rho}{\epsilon_0} | [
{
"order": 1,
"latex": "\\vec{F}_E=q\\vec{E}",
"bbox": [
94,
45,
286,
136
]
},
{
"order": 2,
"latex": "\\frac{\\varphi(n)}{n}",
"bbox": [
94,
176,
276,
398
]
},
{
"order": 3,
"latex": "\\frac{e^{\\cdot\\frac{x^8}{8\\sigm... | |
163985 | human | handwriting | grid | photo | white | 7 | 1,000 | 583 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\overline{f}=f$
${448\cdot246^{452}}^{\frac{2}{148}}$
$\int cose^xdx$
$x_i=\alpha A_{i,j}^Tx_j+e_i$
${284^4}^{\frac{\frac{7}{446}}{4}}$
$45^{45^{45^{45^{43}}}}$
$\frac{\partial x}{\partial u}$ | \overline{f}=f
{448\cdot246^{452}}^{\frac{2}{148}}
\int cose^xdx
x_i=\alpha A_{i,j}^Tx_j+e_i
{284^4}^{\frac{\frac{7}{446}}{4}}
45^{45^{45^{45^{43}}}}
\frac{\partial x}{\partial u} | [
{
"order": 1,
"latex": "\\overline{f}=f",
"bbox": [
48,
52,
212,
186
]
},
{
"order": 2,
"latex": "{448\\cdot246^{452}}^{\\frac{2}{148}}",
"bbox": [
369,
48,
630,
130
]
},
{
"order": 3,
"latex": "\\int cose^xdx",
"bbo... | |
193816 | human | handwriting | twocol | photo | white | 8 | 1,000 | 858 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $b^{(t_j)}$
$\hat{\sigma}_N^2(f)$
$m_{rwl}=\frac{m_0}{\sqrt{7\cdot\frac{g^8}{c^8}}}$
$e^{\lambda(r)}-1=\frac{r_s}{r-r_s}$
$n=\prod_{i=1}^rp_i^{a_i}$
$\begin{bmatrix}a&-y\\b&x\end{bmatrix}$
$w\notin B(v)$
$-\sqrt{\frac{3}{35}}$ | b^{(t_j)}
\hat{\sigma}_N^2(f)
m_{rwl}=\frac{m_0}{\sqrt{7\cdot\frac{g^8}{c^8}}}
e^{\lambda(r)}-1=\frac{r_s}{r-r_s}
n=\prod_{i=1}^rp_i^{a_i}
\begin{bmatrix}a&-y\\b&x\end{bmatrix}
w\notin B(v)
-\sqrt{\frac{3}{35}} | [
{
"order": 1,
"latex": "b^{(t_j)}",
"bbox": [
48,
49,
173,
168
]
},
{
"order": 2,
"latex": "\\hat{\\sigma}_N^2(f)",
"bbox": [
48,
208,
470,
398
]
},
{
"order": 3,
"latex": "m_{rwl}=\\frac{m_0}{\\sqrt{7\\cdot\\frac{g^8}{c... | |
057241 | human | handwriting | numbered | photo | white | 5 | 1,000 | 1,048 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\alpha=\frac{1}{\sqrt{1\cdot\frac{v^7}{c^7}}}$
2) $\frac{\partial r_i}{\partial\beta_j}$
3) $\frac{dP}{dt}$
4) $P=\{P_{\theta}:\theta\in\Theta\}$
5) $\frac{d}{dr}B(r)=-DB$ | \alpha=\frac{1}{\sqrt{1\cdot\frac{v^7}{c^7}}}
\frac{\partial r_i}{\partial\beta_j}
\frac{dP}{dt}
P=\{P_{\theta}:\theta\in\Theta\}
\frac{d}{dr}B(r)=-DB | [
{
"order": 1,
"latex": "\\alpha=\\frac{1}{\\sqrt{1\\cdot\\frac{v^7}{c^7}}}",
"bbox": [
94,
45,
352,
165
]
},
{
"order": 2,
"latex": "\\frac{\\partial r_i}{\\partial\\beta_j}",
"bbox": [
94,
200,
266,
339
]
},
{
"order": 3,
... | |
005034 | human | handwriting | stack | photo | lines | 5 | 1,000 | 980 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\tilde{a}_1,...,\tilde{a}_{m/n}$
$D(\mu):=E[a_{\mu}(X)]$
$7^1/\frac{5^{386}}{\sqrt{108}}$
$\Gamma$
$\binom{n}{k}_q$ | \tilde{a}_1,...,\tilde{a}_{m/n}
D(\mu):=E[a_{\mu}(X)]
7^1/\frac{5^{386}}{\sqrt{108}}
\Gamma
\binom{n}{k}_q | [
{
"order": 1,
"latex": "\\tilde{a}_1,...,\\tilde{a}_{m/n}",
"bbox": [
48,
52,
815,
247
]
},
{
"order": 2,
"latex": "D(\\mu):=E[a_{\\mu}(X)]",
"bbox": [
48,
274,
351,
339
]
},
{
"order": 3,
"latex": "7^1/\\frac{5^{386}}{\... | |
167740 | human | handwriting | stack | photo | lines | 4 | 1,000 | 715 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{dx}{dy}=\frac{1}{y^2}$
$\hat{w}$
$\hat{c_v}_{ln}$
$(\frac{5}{\sqrt{7}})^4\cdot\frac{3}{56}$ | \frac{dx}{dy}=\frac{1}{y^2}
\hat{w}
\hat{c_v}_{ln}
(\frac{5}{\sqrt{7}})^4\cdot\frac{3}{56} | [
{
"order": 1,
"latex": "\\frac{dx}{dy}=\\frac{1}{y^2}",
"bbox": [
48,
47,
344,
277
]
},
{
"order": 2,
"latex": "\\hat{w}",
"bbox": [
48,
321,
98,
372
]
},
{
"order": 3,
"latex": "\\hat{c_v}_{ln}",
"bbox": [
48,... | |
018779 | human | handwriting | numbered | photo | white | 7 | 1,000 | 1,409 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $L\cdot\frac{10.67}{C^{1.85}d^{4.87}}$
2) $\begin{pmatrix}1&1\\0&1\end{pmatrix}$
3) $\tilde{A}_2$
4) $\sigma_f=|a|\sigma_A$
5) $n=\sqrt{2+2k}$
6) $U_L=1-\frac{{\langle s^4\rangle}_L}{3{\langle s^2\rangle}_L^2}$
7) ${7^{112}}^{\frac{\sqrt{5}}{\sqrt{10}}}$ | L\cdot\frac{10.67}{C^{1.85}d^{4.87}}
\begin{pmatrix}1&1\\0&1\end{pmatrix}
\tilde{A}_2
\sigma_f=|a|\sigma_A
n=\sqrt{2+2k}
U_L=1-\frac{{\langle s^4\rangle}_L}{3{\langle s^2\rangle}_L^2}
{7^{112}}^{\frac{\sqrt{5}}{\sqrt{10}}} | [
{
"order": 1,
"latex": "L\\cdot\\frac{10.67}{C^{1.85}d^{4.87}}",
"bbox": [
94,
44,
462,
230
]
},
{
"order": 2,
"latex": "\\begin{pmatrix}1&1\\\\0&1\\end{pmatrix}",
"bbox": [
94,
259,
420,
489
]
},
{
"order": 3,
"latex": ... | |
125012 | human | handwriting | grid | photo | white | 9 | 1,000 | 600 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $q=\frac{pn}{n-p}$
$(\frac{5-205}{29}-\frac{179}{4})$
$\frac{e^{\cdot\frac{(a\cdot t)^2}{6}}}{\sqrt{6\mu}}$
$f(x)=\prod_{i<4}(x-x_i)$
$U^{\otimes r}\otimes(U^{*})^{\otimes s}dU$
$A\rightarrow A^{\prime}=A+\nabla\Lambda$
$u\notin\Phi(V)$
$\alpha_i\simeq-\mu/kT$
$\hat{p}=1$ | q=\frac{pn}{n-p}
(\frac{5-205}{29}-\frac{179}{4})
\frac{e^{\cdot\frac{(a\cdot t)^2}{6}}}{\sqrt{6\mu}}
f(x)=\prod_{i<4}(x-x_i)
U^{\otimes r}\otimes(U^{*})^{\otimes s}dU
A\rightarrow A^{\prime}=A+\nabla\Lambda
u\notin\Phi(V)
\alpha_i\simeq-\mu/kT
\hat{p}=1 | [
{
"order": 1,
"latex": "q=\\frac{pn}{n-p}",
"bbox": [
48,
48,
195,
143
]
},
{
"order": 2,
"latex": "(\\frac{5-205}{29}-\\frac{179}{4})",
"bbox": [
369,
49,
630,
146
]
},
{
"order": 3,
"latex": "\\frac{e^{\\cdot\\frac{(a\... | |
137904 | human | handwriting | twocol | photo | white | 10 | 1,000 | 968 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $x^{lcm(k_1,...,k_m)/k_l}$
$(c-v)\rightarrow c$
$(7/13)$
$x_i=\sum_{j\rightarrow i}\frac{1}{N_j}x_j^{(k)}$
$\frac{dy_1}{dt}=-Ay_1$
$A_{\perp}=\frac{2\pi e\Delta H}{\hbar c}$
$x_n=\frac{1}{n}$
$\frac{2}{6}\cdot\frac{7^6}{5}$
$(\frac{\frac{10}{10}}{118})^{3^{\sqrt{10}}}$
$-\sqrt{\frac{1}{70}}$ | x^{lcm(k_1,...,k_m)/k_l}
(c-v)\rightarrow c
(7/13)
x_i=\sum_{j\rightarrow i}\frac{1}{N_j}x_j^{(k)}
\frac{dy_1}{dt}=-Ay_1
A_{\perp}=\frac{2\pi e\Delta H}{\hbar c}
x_n=\frac{1}{n}
\frac{2}{6}\cdot\frac{7^6}{5}
(\frac{\frac{10}{10}}{118})^{3^{\sqrt{10}}}
-\sqrt{\frac{1}{70}} | [
{
"order": 1,
"latex": "x^{lcm(k_1,...,k_m)/k_l}",
"bbox": [
48,
50,
470,
156
]
},
{
"order": 2,
"latex": "(c-v)\\rightarrow c",
"bbox": [
48,
186,
274,
238
]
},
{
"order": 3,
"latex": "(7/13)",
"bbox": [
48,
... | |
166059 | human | handwriting | numbered | photo | lines | 7 | 1,000 | 1,036 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\frac{\partial V}{\partial r}=\frac{2\pi rh}{3}$
2) $\{w_k\}_{k\in N_0}$
3) $PC_x\subseteq C_x\subseteq QC_x$
4) $n_0=\frac{p_0}{k_BT_0}$
5) $\hat{q}_i$
6) $(132/10+9)\cdot6^{209}-232$
7) $\frac{\frac{c_{n-1}b_n}{c_n}+\frac{c_{n+1}}{c_nb_n}}{2}$ | \frac{\partial V}{\partial r}=\frac{2\pi rh}{3}
\{w_k\}_{k\in N_0}
PC_x\subseteq C_x\subseteq QC_x
n_0=\frac{p_0}{k_BT_0}
\hat{q}_i
(132/10+9)\cdot6^{209}-232
\frac{\frac{c_{n-1}b_n}{c_n}+\frac{c_{n+1}}{c_nb_n}}{2} | [
{
"order": 1,
"latex": "\\frac{\\partial V}{\\partial r}=\\frac{2\\pi rh}{3}",
"bbox": [
94,
51,
271,
254
]
},
{
"order": 2,
"latex": "\\{w_k\\}_{k\\in N_0}",
"bbox": [
94,
288,
241,
338
]
},
{
"order": 3,
"latex": "PC_x... | |
111461 | human | handwriting | numbered | photo | white | 4 | 1,000 | 1,135 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\frac{3^{53}}{(6-4)^9}$
2) $\gamma(n)=\prod_{p|n}p$
3) $\frac{\frac{2}{3}}{{8^6}^6}$
4) $(\frac{(1\cdot1)}{296})^{138^{130}}$ | \frac{3^{53}}{(6-4)^9}
\gamma(n)=\prod_{p|n}p
\frac{\frac{2}{3}}{{8^6}^6}
(\frac{(1\cdot1)}{296})^{138^{130}} | [
{
"order": 1,
"latex": "\\frac{3^{53}}{(6-4)^9}",
"bbox": [
94,
44,
307,
266
]
},
{
"order": 2,
"latex": "\\gamma(n)=\\prod_{p|n}p",
"bbox": [
94,
313,
590,
535
]
},
{
"order": 3,
"latex": "\\frac{\\frac{2}{3}}{{8^6}^6}"... | |
145470 | human | handwriting | grid | photo | grid | 6 | 1,000 | 575 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\hat{B}$
$\tilde{\sigma}_{ij}$
$\frac{1}{2\pi C_i(R_A//R_i)}$
$\frac{n(n-3)}{2}$
$\prod B_{\lambda}$
$(\frac{4}{7}-9)^{204\cdot\sqrt{5}}$ | \hat{B}
\tilde{\sigma}_{ij}
\frac{1}{2\pi C_i(R_A//R_i)}
\frac{n(n-3)}{2}
\prod B_{\lambda}
(\frac{4}{7}-9)^{204\cdot\sqrt{5}} | [
{
"order": 1,
"latex": "\\hat{B}",
"bbox": [
48,
52,
116,
157
]
},
{
"order": 2,
"latex": "\\tilde{\\sigma}_{ij}",
"bbox": [
369,
50,
615,
266
]
},
{
"order": 3,
"latex": "\\frac{1}{2\\pi C_i(R_A//R_i)}",
"bbox": [
... | |
078061 | human | handwriting | grid | photo | white | 6 | 1,000 | 367 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $tanhx=\frac{2t}{1+t^2}$
$\int_0^13x^2+2x+5dt$
$\begin{pmatrix}x&y\\0&z\end{pmatrix}$
$(2^{317}-3)+(\frac{157}{456})^{215}$
$+\sqrt{3}$
$\hat{a}_2,\hat{a}_3$ | tanhx=\frac{2t}{1+t^2}
\int_0^13x^2+2x+5dt
\begin{pmatrix}x&y\\0&z\end{pmatrix}
(2^{317}-3)+(\frac{157}{456})^{215}
+\sqrt{3}
\hat{a}_2,\hat{a}_3 | [
{
"order": 1,
"latex": "tanhx=\\frac{2t}{1+t^2}",
"bbox": [
48,
45,
309,
124
]
},
{
"order": 2,
"latex": "\\int_0^13x^2+2x+5dt",
"bbox": [
369,
49,
630,
116
]
},
{
"order": 3,
"latex": "\\begin{pmatrix}x&y\\\\0&z\\end{pm... | |
022910 | human | handwriting | numbered | photo | white | 5 | 1,000 | 963 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\frac{470^{10}}{7+9^5}$
2) $3\sqrt{2}$
3) $\hat{d}(n)$
4) $(f_U^{\prime},U^{\prime})$
5) $(\sqrt{2})^{log_{\sqrt{2}}3}=3$ | \frac{470^{10}}{7+9^5}
3\sqrt{2}
\hat{d}(n)
(f_U^{\prime},U^{\prime})
(\sqrt{2})^{log_{\sqrt{2}}3}=3 | [
{
"order": 1,
"latex": "\\frac{470^{10}}{7+9^5}",
"bbox": [
94,
47,
421,
266
]
},
{
"order": 2,
"latex": "3\\sqrt{2}",
"bbox": [
94,
313,
321,
438
]
},
{
"order": 3,
"latex": "\\hat{d}(n)",
"bbox": [
94,
... | |
081502 | human | handwriting | numbered | photo | lines | 6 | 1,000 | 1,326 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $p_n\#=\prod_{k=1}^np_k$
2) $\epsilon_l=\frac{eB}{m^{*}}(l+\frac{1}{2})$
3) $\frac{|SD|}{|CD|}=\frac{|SB|}{|AB|}$
4) $\hat{\beta}=(\overline{y/x})$
5) $\int_i^{\infty}1/s^2$
6) $2y\frac{dy}{dx}=3x^2-1$ | p_n\#=\prod_{k=1}^np_k
\epsilon_l=\frac{eB}{m^{*}}(l+\frac{1}{2})
\frac{|SD|}{|CD|}=\frac{|SB|}{|AB|}
\hat{\beta}=(\overline{y/x})
\int_i^{\infty}1/s^2
2y\frac{dy}{dx}=3x^2-1 | [
{
"order": 1,
"latex": "p_n\\#=\\prod_{k=1}^np_k",
"bbox": [
94,
49,
480,
180
]
},
{
"order": 2,
"latex": "\\epsilon_l=\\frac{eB}{m^{*}}(l+\\frac{1}{2})",
"bbox": [
94,
224,
746,
433
]
},
{
"order": 3,
"latex": "\\frac{|... | |
062832 | human | handwriting | stack | photo | lines | 4 | 1,000 | 914 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{1}{d(w)+d(v)}$
$3^{3^{3^{3^{46}}}}$
$\frac{24/\sqrt{3}}{{\sqrt{169}^{98}}^5}$
$\frac{\frac{9}{160}}{323^{339}\cdot\sqrt{383}}$ | \frac{1}{d(w)+d(v)}
3^{3^{3^{3^{46}}}}
\frac{24/\sqrt{3}}{{\sqrt{169}^{98}}^5}
\frac{\frac{9}{160}}{323^{339}\cdot\sqrt{383}} | [
{
"order": 1,
"latex": "\\frac{1}{d(w)+d(v)}",
"bbox": [
48,
49,
322,
165
]
},
{
"order": 2,
"latex": "3^{3^{3^{3^{46}}}}",
"bbox": [
48,
188,
217,
337
]
},
{
"order": 3,
"latex": "\\frac{24/\\sqrt{3}}{{\\sqrt{169}^{98}}... | |
172433 | human | handwriting | stack | photo | lines | 4 | 1,000 | 721 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\overline{s}\in\alpha,t\notin\gamma$
$[X_0:X_1:\cdot\cdot\cdot:X_n]$
$\frac{1}{R_f+R_2}$
$t=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\tau$ | \overline{s}\in\alpha,t\notin\gamma
[X_0:X_1:\cdot\cdot\cdot:X_n]
\frac{1}{R_f+R_2}
t=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\tau | [
{
"order": 1,
"latex": "\\overline{s}\\in\\alpha,t\\notin\\gamma",
"bbox": [
48,
51,
434,
158
]
},
{
"order": 2,
"latex": "[X_0:X_1:\\cdot\\cdot\\cdot:X_n]",
"bbox": [
48,
192,
374,
268
]
},
{
"order": 3,
"latex": "\\fra... | |
127358 | human | handwriting | numbered | photo | lines | 4 | 1,000 | 838 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\wedge,\vee$
2) $Z=-\frac{u_{*}^3}{\Pi\frac{e}{\overline{\theta_j}}\overline{q^{\prime}\theta_j^{\prime}}}$
3) $\begin{bmatrix}17&23\\11&7\end{bmatrix}$
4) $\frac{du}{dr}=-\frac{1}{4\pi r^2}$ | \wedge,\vee
Z=-\frac{u_{*}^3}{\Pi\frac{e}{\overline{\theta_j}}\overline{q^{\prime}\theta_j^{\prime}}}
\begin{bmatrix}17&23\\11&7\end{bmatrix}
\frac{du}{dr}=-\frac{1}{4\pi r^2} | [
{
"order": 1,
"latex": "\\wedge,\\vee",
"bbox": [
94,
51,
315,
144
]
},
{
"order": 2,
"latex": "Z=-\\frac{u_{*}^3}{\\Pi\\frac{e}{\\overline{\\theta_j}}\\overline{q^{\\prime}\\theta_j^{\\prime}}}",
"bbox": [
94,
179,
239,
277
]
},
... | |
191526 | human | handwriting | numbered | photo | lines | 7 | 1,000 | 1,224 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $(\xi,\tau;\xi^{\prime},\tau^{\prime})$
2) $k_T\frac{1}{T}\nabla T$
3) $\int d\Omega$
4) $\Delta s=\frac{\lambda}{2sin\varphi}$
5) ${{31^{122}}^4}^{290^{220}}$
6) $x_3=\frac{b}{a}$
7) $\tilde{f}^{*}$ | (\xi,\tau;\xi^{\prime},\tau^{\prime})
k_T\frac{1}{T}\nabla T
\int d\Omega
\Delta s=\frac{\lambda}{2sin\varphi}
{{31^{122}}^4}^{290^{220}}
x_3=\frac{b}{a}
\tilde{f}^{*} | [
{
"order": 1,
"latex": "(\\xi,\\tau;\\xi^{\\prime},\\tau^{\\prime})",
"bbox": [
94,
51,
264,
108
]
},
{
"order": 2,
"latex": "k_T\\frac{1}{T}\\nabla T",
"bbox": [
94,
149,
409,
259
]
},
{
"order": 3,
"latex": "\\int d\\O... | |
102879 | human | handwriting | grid | photo | white | 7 | 1,000 | 506 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\tilde{B}_5$
$q_e=\frac{q_b}{\sqrt{\frac{q_b}{q_m}}}$
$\int_0^{\infty}f(x)dx$
$G(t)=\int_0^tg(s)ds$
$B_{MX}^{\phi}$
$E_z=\frac{I}{||I||}=\frac{I}{\sqrt{3}}$
$\zeta(s)=\overline{\zeta(\overline{s})}$ | \tilde{B}_5
q_e=\frac{q_b}{\sqrt{\frac{q_b}{q_m}}}
\int_0^{\infty}f(x)dx
G(t)=\int_0^tg(s)ds
B_{MX}^{\phi}
E_z=\frac{I}{||I||}=\frac{I}{\sqrt{3}}
\zeta(s)=\overline{\zeta(\overline{s})} | [
{
"order": 1,
"latex": "\\tilde{B}_5",
"bbox": [
48,
47,
151,
174
]
},
{
"order": 2,
"latex": "q_e=\\frac{q_b}{\\sqrt{\\frac{q_b}{q_m}}}",
"bbox": [
369,
49,
563,
203
]
},
{
"order": 3,
"latex": "\\int_0^{\\infty}f(x)dx"... | |
161015 | human | handwriting | stack | photo | white | 5 | 1,000 | 844 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{2}{\sqrt{k}}$
$f(\underline{m})=0$
$1.79\pm0.01$
$\frac{1}{\sqrt{3}}(1,1,1)$
$|E_{-}\rangle$ | \frac{2}{\sqrt{k}}
f(\underline{m})=0
1.79\pm0.01
\frac{1}{\sqrt{3}}(1,1,1)
|E_{-}\rangle | [
{
"order": 1,
"latex": "\\frac{2}{\\sqrt{k}}",
"bbox": [
48,
44,
148,
141
]
},
{
"order": 2,
"latex": "f(\\underline{m})=0",
"bbox": [
48,
193,
273,
327
]
},
{
"order": 3,
"latex": "1.79\\pm0.01",
"bbox": [
48,... | |
047081 | human | handwriting | stack | photo | lines | 5 | 1,000 | 802 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\omega,\phi\rightarrow\pi^0\pi^0\gamma$
$w=\frac{mv}{\sqrt{5-\frac{v^6}{h^6}}}$
$1:\sqrt{\varphi}:\varphi$
$Bk_BT_{sys}$
$Re\langle Ax,x\rangle\leq0$ | \omega,\phi\rightarrow\pi^0\pi^0\gamma
w=\frac{mv}{\sqrt{5-\frac{v^6}{h^6}}}
1:\sqrt{\varphi}:\varphi
Bk_BT_{sys}
Re\langle Ax,x\rangle\leq0 | [
{
"order": 1,
"latex": "\\omega,\\phi\\rightarrow\\pi^0\\pi^0\\gamma",
"bbox": [
48,
49,
355,
123
]
},
{
"order": 2,
"latex": "w=\\frac{mv}{\\sqrt{5-\\frac{v^6}{h^6}}}",
"bbox": [
48,
159,
298,
282
]
},
{
"order": 3,
"la... | |
064611 | human | handwriting | grid | photo | grid | 6 | 1,000 | 559 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $1-\frac{0.91^2}{1.09}=0.240$
$\int_x^xf(t)dt=0$
$(\frac{\frac{297}{265}}{419})^{5^7}$
$W\underline{A}$
$\tilde{D}_4$
$lim_{n\rightarrow\infty}H_n^k$ | 1-\frac{0.91^2}{1.09}=0.240
\int_x^xf(t)dt=0
(\frac{\frac{297}{265}}{419})^{5^7}
W\underline{A}
\tilde{D}_4
lim_{n\rightarrow\infty}H_n^k | [
{
"order": 1,
"latex": "1-\\frac{0.91^2}{1.09}=0.240",
"bbox": [
48,
50,
309,
167
]
},
{
"order": 2,
"latex": "\\int_x^xf(t)dt=0",
"bbox": [
369,
51,
630,
141
]
},
{
"order": 3,
"latex": "(\\frac{\\frac{297}{265}}{419})^... | |
080665 | human | handwriting | numbered | photo | lines | 4 | 1,000 | 683 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $\int_0^{x_0}sinxdx$
2) $\frac{\partial}{\partial x_{ij}}$
3) $dW(t)=N(t)dt$
4) $\hat{k}$ | \int_0^{x_0}sinxdx
\frac{\partial}{\partial x_{ij}}
dW(t)=N(t)dt
\hat{k} | [
{
"order": 1,
"latex": "\\int_0^{x_0}sinxdx",
"bbox": [
94,
50,
264,
116
]
},
{
"order": 2,
"latex": "\\frac{\\partial}{\\partial x_{ij}}",
"bbox": [
94,
156,
249,
378
]
},
{
"order": 3,
"latex": "dW(t)=N(t)dt",
"bbo... | |
054167 | human | handwriting | stack | photo | white | 4 | 1,000 | 732 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\sqrt{53}^{\sqrt{9}}-\frac{494}{\sqrt{8}}$
$C=cos(\theta)$
$A=4A_0=\sqrt{3}a^2$
$r_m=\frac{r_2+r_1}{2}(13)$ | \sqrt{53}^{\sqrt{9}}-\frac{494}{\sqrt{8}}
C=cos(\theta)
A=4A_0=\sqrt{3}a^2
r_m=\frac{r_2+r_1}{2}(13) | [
{
"order": 1,
"latex": "\\sqrt{53}^{\\sqrt{9}}-\\frac{494}{\\sqrt{8}}",
"bbox": [
48,
46,
581,
268
]
},
{
"order": 2,
"latex": "C=cos(\\theta)",
"bbox": [
48,
313,
498,
436
]
},
{
"order": 3,
"latex": "A=4A_0=\\sqrt{3}a^... | |
123872 | human | handwriting | numbered | photo | white | 6 | 1,000 | 1,073 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $-\overline{v^{\prime}T^{\prime}}$
2) $E=\frac{mz^3}{\sqrt{1+\frac{f^3}{z^3}}}$
3) $\frac{a^2}{2L}$
4) $Re=\frac{vL\rho}{\mu}$
5) $(\frac{ij}{i+j})$
6) $lp_b=\frac{lm_bv_b}{\sqrt{3+\frac{v_b^2}{o^2}}}$ | -\overline{v^{\prime}T^{\prime}}
E=\frac{mz^3}{\sqrt{1+\frac{f^3}{z^3}}}
\frac{a^2}{2L}
Re=\frac{vL\rho}{\mu}
(\frac{ij}{i+j})
lp_b=\frac{lm_bv_b}{\sqrt{3+\frac{v_b^2}{o^2}}} | [
{
"order": 1,
"latex": "-\\overline{v^{\\prime}T^{\\prime}}",
"bbox": [
94,
48,
529,
241
]
},
{
"order": 2,
"latex": "E=\\frac{mz^3}{\\sqrt{1+\\frac{f^3}{z^3}}}",
"bbox": [
94,
269,
259,
392
]
},
{
"order": 3,
"latex": "... | |
149136 | human | handwriting | numbered | photo | lines | 6 | 1,000 | 1,249 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $W_{\alpha}\equiv\overline{D}^2D_{\alpha}V$
2) $x(t)=\frac{1}{t_c-t}$
3) $\frac{V_{max}}{\frac{8}{8\cdot\frac{[U]}{[U]+Z_i}}}$
4) $E=V_0$
5) $\frac{10^{143}}{4-2^6}$
6) $\begin{pmatrix}k&\frac{d}{nk}\\0&\frac{1}{k}\end{pmatrix}$ | W_{\alpha}\equiv\overline{D}^2D_{\alpha}V
x(t)=\frac{1}{t_c-t}
\frac{V_{max}}{\frac{8}{8\cdot\frac{[U]}{[U]+Z_i}}}
E=V_0
\frac{10^{143}}{4-2^6}
\begin{pmatrix}k&\frac{d}{nk}\\0&\frac{1}{k}\end{pmatrix} | [
{
"order": 1,
"latex": "W_{\\alpha}\\equiv\\overline{D}^2D_{\\alpha}V",
"bbox": [
94,
44,
857,
269
]
},
{
"order": 2,
"latex": "x(t)=\\frac{1}{t_c-t}",
"bbox": [
94,
310,
421,
412
]
},
{
"order": 3,
"latex": "\\frac{V_{m... | |
142511 | human | handwriting | numbered | photo | lines | 7 | 1,000 | 1,365 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $2^{2^{2^2}}=65536$
2) $x=\frac{r\mu\nu}{bc}$
3) $\frac{\frac{1}{5}}{2+5}$
4) $forRe(x)\geq\frac{1}{2}$
5) $E=\frac{m+y^7}{\sqrt{1-\frac{|e|^7}{y^7}}}$
6) $\dot{\rho}=-3\frac{\dot{a}}{a}(\rho+\frac{p}{c^2})$
7) $\frac{\lambda(1+\nu)(1-2\nu)}{\nu}$ | 2^{2^{2^2}}=65536
x=\frac{r\mu\nu}{bc}
\frac{\frac{1}{5}}{2+5}
forRe(x)\geq\frac{1}{2}
E=\frac{m+y^7}{\sqrt{1-\frac{|e|^7}{y^7}}}
\dot{\rho}=-3\frac{\dot{a}}{a}(\rho+\frac{p}{c^2})
\frac{\lambda(1+\nu)(1-2\nu)}{\nu} | [
{
"order": 1,
"latex": "2^{2^{2^2}}=65536",
"bbox": [
94,
51,
687,
208
]
},
{
"order": 2,
"latex": "x=\\frac{r\\mu\\nu}{bc}",
"bbox": [
94,
238,
259,
320
]
},
{
"order": 3,
"latex": "\\frac{\\frac{1}{5}}{2+5}",
"bbox... | |
142024 | human | handwriting | stack | photo | lines | 4 | 1,000 | 947 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\tilde{H}_r$
$7^{7^{\cdot^{\cdot^{\cdot^j}}}}$
$s\begin{Bmatrix}4\\3\end{Bmatrix}$
$\pi h^2=\frac{16\pi}{3}$ | \tilde{H}_r
7^{7^{\cdot^{\cdot^{\cdot^j}}}}
s\begin{Bmatrix}4\\3\end{Bmatrix}
\pi h^2=\frac{16\pi}{3} | [
{
"order": 1,
"latex": "\\tilde{H}_r",
"bbox": [
48,
52,
138,
144
]
},
{
"order": 2,
"latex": "7^{7^{\\cdot^{\\cdot^{\\cdot^j}}}}",
"bbox": [
48,
174,
308,
402
]
},
{
"order": 3,
"latex": "s\\begin{Bmatrix}4\\\\3\\end{Bm... | |
009781 | human | handwriting | grid | photo | grid | 9 | 1,000 | 773 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\tilde{\phi}$
$\frac{x(A)}{1-x(A)}$
$F=\{(A_i,B_i)\}_{i=1}^h$
$\delta=\frac{2\epsilon\rho}{3D_0}$
${{1^9}^{397}}^{\frac{5\cdot117}{481}}$
$tan\theta=\frac{S_1/\sqrt{n_1}}{S_2/\sqrt{n_2}}$
$\int\frac{e^x}{x}dx$
$\Theta=\frac{1}{\sqrt{\sum_{\mu=1}^k\frac{g^6}{b_{\mu}^6}}}$
$B^{\prime}\in\binom{C}{B}$ | \tilde{\phi}
\frac{x(A)}{1-x(A)}
F=\{(A_i,B_i)\}_{i=1}^h
\delta=\frac{2\epsilon\rho}{3D_0}
{{1^9}^{397}}^{\frac{5\cdot117}{481}}
tan\theta=\frac{S_1/\sqrt{n_1}}{S_2/\sqrt{n_2}}
\int\frac{e^x}{x}dx
\Theta=\frac{1}{\sqrt{\sum_{\mu=1}^k\frac{g^6}{b_{\mu}^6}}}
B^{\prime}\in\binom{C}{B} | [
{
"order": 1,
"latex": "\\tilde{\\phi}",
"bbox": [
48,
46,
180,
255
]
},
{
"order": 2,
"latex": "\\frac{x(A)}{1-x(A)}",
"bbox": [
369,
51,
625,
252
]
},
{
"order": 3,
"latex": "F=\\{(A_i,B_i)\\}_{i=1}^h",
"bbox": [
... | |
076031 | human | handwriting | numbered | photo | lines | 6 | 1,000 | 1,314 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $(\frac{7^{258}}{270})^{\frac{6}{50}}$
2) $\varphi_{\delta}^6$
3) $\int(u-v)dx$
4) $\int K(x-y;T)dy=1$
5) $\int f=1$
6) $s\begin{Bmatrix}8\\4\end{Bmatrix}$ | (\frac{7^{258}}{270})^{\frac{6}{50}}
\varphi_{\delta}^6
\int(u-v)dx
\int K(x-y;T)dy=1
\int f=1
s\begin{Bmatrix}8\\4\end{Bmatrix} | [
{
"order": 1,
"latex": "(\\frac{7^{258}}{270})^{\\frac{6}{50}}",
"bbox": [
94,
48,
558,
284
]
},
{
"order": 2,
"latex": "\\varphi_{\\delta}^6",
"bbox": [
94,
319,
194,
440
]
},
{
"order": 3,
"latex": "\\int(u-v)dx",
... | |
038681 | human | handwriting | grid | photo | grid | 8 | 1,000 | 591 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\begin{bmatrix}x&=&p\\y&=&p\end{bmatrix}$
$p_i(q_i,\dot{q}_i,t)=\frac{\partial L}{\partial\dot{q}_i}$
$\frac{log(9*0.75)}{log(3)}$
$J=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$
$g_iH=g_jH$
$\Delta P=f_D\frac{\rho V^2}{2}\frac{L}{D}$
$q(x)\approx(\frac{x-r}{2601-r})^5$
$(232^{429}\cdot4^{431})$ | \begin{bmatrix}x&=&p\\y&=&p\end{bmatrix}
p_i(q_i,\dot{q}_i,t)=\frac{\partial L}{\partial\dot{q}_i}
\frac{log(9*0.75)}{log(3)}
J=\begin{bmatrix}0&1\\-1&0\end{bmatrix}
g_iH=g_jH
\Delta P=f_D\frac{\rho V^2}{2}\frac{L}{D}
q(x)\approx(\frac{x-r}{2601-r})^5
(232^{429}\cdot4^{431}) | [
{
"order": 1,
"latex": "\\begin{bmatrix}x&=&p\\\\y&=&p\\end{bmatrix}",
"bbox": [
48,
47,
263,
161
]
},
{
"order": 2,
"latex": "p_i(q_i,\\dot{q}_i,t)=\\frac{\\partial L}{\\partial\\dot{q}_i}",
"bbox": [
369,
48,
630,
147
]
},
{
... | |
026588 | human | handwriting | twocol | photo | white | 10 | 1,000 | 1,112 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $p=\frac{m_8f}{\sqrt{5-\frac{f^2}{n^2}}}$
$\frac{\partial u}{\partial t}=0$
$C_1,C_2,C_3$
$\alpha=\sqrt{\beta^2-1}$
$\frac{(\frac{245}{111})^{102}}{82\cdot481}$
$D=\prod_{i=1}^nD_i$
$\nu=1-\frac{n}{2pn\pm1}$
$\frac{1+\sqrt{5}}{4}$
$\begin{bmatrix}d+1\\k\end{bmatrix}$
$\frac{x^2-1}{x-2}$ | p=\frac{m_8f}{\sqrt{5-\frac{f^2}{n^2}}}
\frac{\partial u}{\partial t}=0
C_1,C_2,C_3
\alpha=\sqrt{\beta^2-1}
\frac{(\frac{245}{111})^{102}}{82\cdot481}
D=\prod_{i=1}^nD_i
\nu=1-\frac{n}{2pn\pm1}
\frac{1+\sqrt{5}}{4}
\begin{bmatrix}d+1\\k\end{bmatrix}
\frac{x^2-1}{x-2} | [
{
"order": 1,
"latex": "p=\\frac{m_8f}{\\sqrt{5-\\frac{f^2}{n^2}}}",
"bbox": [
48,
52,
312,
270
]
},
{
"order": 2,
"latex": "\\frac{\\partial u}{\\partial t}=0",
"bbox": [
48,
295,
417,
527
]
},
{
"order": 3,
"latex": "C... | |
063704 | human | handwriting | numbered | photo | white | 4 | 1,000 | 1,004 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $(\frac{\frac{334}{332}}{6})^{37+255}$
2) $\frac{\frac{(39\cdot3)}{6}}{189^{220}}$
3) $n=\binom{2k-1}{k}$
4) $\begin{pmatrix}1&0\\0&N\end{pmatrix}$ | (\frac{\frac{334}{332}}{6})^{37+255}
\frac{\frac{(39\cdot3)}{6}}{189^{220}}
n=\binom{2k-1}{k}
\begin{pmatrix}1&0\\0&N\end{pmatrix} | [
{
"order": 1,
"latex": "(\\frac{\\frac{334}{332}}{6})^{37+255}",
"bbox": [
94,
48,
613,
276
]
},
{
"order": 2,
"latex": "\\frac{\\frac{(39\\cdot3)}{6}}{189^{220}}",
"bbox": [
94,
306,
240,
528
]
},
{
"order": 3,
"latex":... | |
180878 | human | handwriting | twocol | photo | white | 10 | 1,000 | 1,241 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\binom{k}{2}-m$
$(\frac{127-4}{7})^{\frac{100^{168}}{370}}$
$\int_0^{t_1}E(t)dt$
$\int_X\int_Y\int_Z$
$r=\frac{1}{2}\sqrt{ab}$
$\begin{Bmatrix}q+p\\r\end{Bmatrix}$
$\hat{\Phi}$
$C_u=\frac{D_{60}}{D_{10}}$
$\tilde{O}(log^4q)$
$P\times\frac{n}{N}$ | \binom{k}{2}-m
(\frac{127-4}{7})^{\frac{100^{168}}{370}}
\int_0^{t_1}E(t)dt
\int_X\int_Y\int_Z
r=\frac{1}{2}\sqrt{ab}
\begin{Bmatrix}q+p\\r\end{Bmatrix}
\hat{\Phi}
C_u=\frac{D_{60}}{D_{10}}
\tilde{O}(log^4q)
P\times\frac{n}{N} | [
{
"order": 1,
"latex": "\\binom{k}{2}-m",
"bbox": [
48,
49,
427,
238
]
},
{
"order": 2,
"latex": "(\\frac{127-4}{7})^{\\frac{100^{168}}{370}}",
"bbox": [
48,
274,
403,
504
]
},
{
"order": 3,
"latex": "\\int_0^{t_1}E(t)dt... | |
099131 | human | handwriting | grid | photo | white | 6 | 1,000 | 509 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | ${9^9}^{\frac{9}{5}}$
$\frac{\partial L}{\partial f_t}$
$H=log_b|M|$
$U=\begin{pmatrix}0&1\\1&0\end{pmatrix}$
$\int cos(x^2)dx$
$n=\frac{log_{10}(\frac{L}{l})}{log_{10}(2)}$ | {9^9}^{\frac{9}{5}}
\frac{\partial L}{\partial f_t}
H=log_b|M|
U=\begin{pmatrix}0&1\\1&0\end{pmatrix}
\int cos(x^2)dx
n=\frac{log_{10}(\frac{L}{l})}{log_{10}(2)} | [
{
"order": 1,
"latex": "{9^9}^{\\frac{9}{5}}",
"bbox": [
48,
50,
179,
256
]
},
{
"order": 2,
"latex": "\\frac{\\partial L}{\\partial f_t}",
"bbox": [
369,
51,
473,
193
]
},
{
"order": 3,
"latex": "H=log_b|M|",
"bbox"... | |
056131 | human | handwriting | stack | photo | lines | 5 | 1,000 | 927 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{\partial r_i}{\partial\beta_j}$
$\sigma=\sqrt{\frac{\mu(1-\mu)}{3+51}}$
$O=\frac{m\cdot t^2}{\sqrt{9+\frac{|v|^2}{t^2}}}$
$h(\underline{n})=h^{*}(-\underline{n})$
$(138+406)^{\frac{2}{10}}$ | \frac{\partial r_i}{\partial\beta_j}
\sigma=\sqrt{\frac{\mu(1-\mu)}{3+51}}
O=\frac{m\cdot t^2}{\sqrt{9+\frac{|v|^2}{t^2}}}
h(\underline{n})=h^{*}(-\underline{n})
(138+406)^{\frac{2}{10}} | [
{
"order": 1,
"latex": "\\frac{\\partial r_i}{\\partial\\beta_j}",
"bbox": [
48,
49,
147,
177
]
},
{
"order": 2,
"latex": "\\sigma=\\sqrt{\\frac{\\mu(1-\\mu)}{3+51}}",
"bbox": [
48,
221,
471,
379
]
},
{
"order": 3,
"late... | |
059213 | human | handwriting | stack | photo | lines | 5 | 1,000 | 1,208 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\theta=\frac{t-\pi}{2}$
$\frac{(\frac{3}{361})^{\sqrt{9}}}{\frac{\sqrt{7}}{297}}$
$\frac{dy}{y}=-f(t)dt$
$10^{-1024}$
$A=\begin{bmatrix}2&-2\\-2&1\end{bmatrix}$ | \theta=\frac{t-\pi}{2}
\frac{(\frac{3}{361})^{\sqrt{9}}}{\frac{\sqrt{7}}{297}}
\frac{dy}{y}=-f(t)dt
10^{-1024}
A=\begin{bmatrix}2&-2\\-2&1\end{bmatrix} | [
{
"order": 1,
"latex": "\\theta=\\frac{t-\\pi}{2}",
"bbox": [
48,
45,
494,
277
]
},
{
"order": 2,
"latex": "\\frac{(\\frac{3}{361})^{\\sqrt{9}}}{\\frac{\\sqrt{7}}{297}}",
"bbox": [
48,
324,
284,
552
]
},
{
"order": 3,
"l... | |
074168 | human | handwriting | stack | photo | white | 4 | 1,000 | 832 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $-\overline{u}$
$f(a)=\prod q_i^{n_i}$
$\frac{\frac{\sqrt{131}}{3}}{(454-1)\cdot7}$
$\frac{(394+1)}{\frac{\frac{3}{184}}{102}}$ | -\overline{u}
f(a)=\prod q_i^{n_i}
\frac{\frac{\sqrt{131}}{3}}{(454-1)\cdot7}
\frac{(394+1)}{\frac{\frac{3}{184}}{102}} | [
{
"order": 1,
"latex": "-\\overline{u}",
"bbox": [
48,
50,
190,
113
]
},
{
"order": 2,
"latex": "f(a)=\\prod q_i^{n_i}",
"bbox": [
48,
149,
365,
255
]
},
{
"order": 3,
"latex": "\\frac{\\frac{\\sqrt{131}}{3}}{(454-1)\\cd... | |
034132 | human | handwriting | numbered | photo | lines | 7 | 1,000 | 1,352 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $|1\rangle=\binom{0}{1}$
2) $\frac{d^2r}{ds^2}+\alpha r=-P$
3) $\frac{(331/294)\cdot463}{\frac{\frac{13}{8}}{2}}$
4) $\int-2r^2sin(u)du$
5) $\binom{n-1}{i}$
6) $\binom{4}{2}$
7) $\prod_{p^k|n}f(p^k)$ | |1\rangle=\binom{0}{1}
\frac{d^2r}{ds^2}+\alpha r=-P
\frac{(331/294)\cdot463}{\frac{\frac{13}{8}}{2}}
\int-2r^2sin(u)du
\binom{n-1}{i}
\binom{4}{2}
\prod_{p^k|n}f(p^k) | [
{
"order": 1,
"latex": "|1\\rangle=\\binom{0}{1}",
"bbox": [
94,
48,
365,
189
]
},
{
"order": 2,
"latex": "\\frac{d^2r}{ds^2}+\\alpha r=-P",
"bbox": [
94,
232,
497,
370
]
},
{
"order": 3,
"latex": "\\frac{(331/294)\\cdot... | |
145232 | human | handwriting | stack | photo | white | 5 | 1,000 | 1,062 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\int f^{\prime}(x)dx$
$k\equiv\frac{R}{4a}$
$\binom{n+x-1}{n}$
$(\frac{5}{\sqrt{292}})^{195}-455^9+5$
$cosA=\frac{a}{c}$ | \int f^{\prime}(x)dx
k\equiv\frac{R}{4a}
\binom{n+x-1}{n}
(\frac{5}{\sqrt{292}})^{195}-455^9+5
cosA=\frac{a}{c} | [
{
"order": 1,
"latex": "\\int f^{\\prime}(x)dx",
"bbox": [
48,
50,
442,
272
]
},
{
"order": 2,
"latex": "k\\equiv\\frac{R}{4a}",
"bbox": [
48,
316,
238,
443
]
},
{
"order": 3,
"latex": "\\binom{n+x-1}{n}",
"bbox": [
... | |
160939 | human | handwriting | grid | photo | grid | 6 | 1,000 | 371 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\sqrt{\Theta}$
$\frac{4\times8}{1081}\approx0.0296$
$E\{\hat{x}-x\}=0$
$z^{z^{\cdot^{\cdot^{z^z}}}}$
$\hat{T}$
$p_{s1}=\gamma_sT_{s0}n_{s1}$ | \sqrt{\Theta}
\frac{4\times8}{1081}\approx0.0296
E\{\hat{x}-x\}=0
z^{z^{\cdot^{\cdot^{z^z}}}}
\hat{T}
p_{s1}=\gamma_sT_{s0}n_{s1} | [
{
"order": 1,
"latex": "\\sqrt{\\Theta}",
"bbox": [
48,
50,
168,
145
]
},
{
"order": 2,
"latex": "\\frac{4\\times8}{1081}\\approx0.0296",
"bbox": [
369,
52,
583,
141
]
},
{
"order": 3,
"latex": "E\\{\\hat{x}-x\\}=0",
... | |
071024 | human | handwriting | grid | photo | grid | 8 | 1,000 | 816 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\sqrt{x+1}$
$\int_2^5x^2dx$
$\frac{R_3}{R_1}=\frac{R_a}{R_c}$
$n=\prod_{i=1}^rp_i^{a_i}$
$V=100\frac{(L-U)}{(L-H)}$
$\frac{\frac{10^{10}}{113}}{\frac{4}{6}}$
$\binom{n}{4}$
$\mathbb{H}$ | \sqrt{x+1}
\int_2^5x^2dx
\frac{R_3}{R_1}=\frac{R_a}{R_c}
n=\prod_{i=1}^rp_i^{a_i}
V=100\frac{(L-U)}{(L-H)}
\frac{\frac{10^{10}}{113}}{\frac{4}{6}}
\binom{n}{4}
\mathbb{H} | [
{
"order": 1,
"latex": "\\sqrt{x+1}",
"bbox": [
48,
51,
309,
166
]
},
{
"order": 2,
"latex": "\\int_2^5x^2dx",
"bbox": [
369,
50,
630,
223
]
},
{
"order": 3,
"latex": "\\frac{R_3}{R_1}=\\frac{R_a}{R_c}",
"bbox": [
... | |
022520 | human | handwriting | stack | photo | white | 4 | 1,000 | 698 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $E^{*}=\frac{E}{1-\nu^2}$
$\frac{\frac{5}{398}}{\frac{141^5}{304}}$
$g_{ab}$
$r=\frac{l}{1+ecos\theta}$ | E^{*}=\frac{E}{1-\nu^2}
\frac{\frac{5}{398}}{\frac{141^5}{304}}
g_{ab}
r=\frac{l}{1+ecos\theta} | [
{
"order": 1,
"latex": "E^{*}=\\frac{E}{1-\\nu^2}",
"bbox": [
48,
45,
294,
146
]
},
{
"order": 2,
"latex": "\\frac{\\frac{5}{398}}{\\frac{141^5}{304}}",
"bbox": [
48,
194,
149,
334
]
},
{
"order": 3,
"latex": "g_{ab}",
... | |
193234 | human | handwriting | numbered | photo | lines | 5 | 1,000 | 1,053 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $B_{\tilde{\nu}}$
2) $m=\frac{5\beta_2-9}{2(3-\beta_2)}$
3) $f^{i^{c^{\cdot^{\cdot^{\cdot}}}}}$
4) $A=\begin{pmatrix}1&2\\3&4\end{pmatrix}$
5) $v_{22}=1$ | B_{\tilde{\nu}}
m=\frac{5\beta_2-9}{2(3-\beta_2)}
f^{i^{c^{\cdot^{\cdot^{\cdot}}}}}
A=\begin{pmatrix}1&2\\3&4\end{pmatrix}
v_{22}=1 | [
{
"order": 1,
"latex": "B_{\\tilde{\\nu}}",
"bbox": [
94,
52,
267,
207
]
},
{
"order": 2,
"latex": "m=\\frac{5\\beta_2-9}{2(3-\\beta_2)}",
"bbox": [
94,
251,
476,
375
]
},
{
"order": 3,
"latex": "f^{i^{c^{\\cdot^{\\cdot^... | |
099777 | human | handwriting | numbered | photo | lines | 7 | 1,000 | 1,147 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $OB$
2) $q^{\prime}\notin\delta(q,a)$
3) $\hat{G}(z)$
4) $\tilde{h}(I)$
5) $\prod_{i=2}^{2002}1$
6) $\sqrt{t}$
7) $\omega=\frac{\hbar k^2}{2m}$ | OB
q^{\prime}\notin\delta(q,a)
\hat{G}(z)
\tilde{h}(I)
\prod_{i=2}^{2002}1
\sqrt{t}
\omega=\frac{\hbar k^2}{2m} | [
{
"order": 1,
"latex": "OB",
"bbox": [
94,
51,
249,
150
]
},
{
"order": 2,
"latex": "q^{\\prime}\\notin\\delta(q,a)",
"bbox": [
94,
172,
475,
284
]
},
{
"order": 3,
"latex": "\\hat{G}(z)",
"bbox": [
94,
3... | |
102994 | human | handwriting | numbered | photo | white | 6 | 1,000 | 1,180 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $u=\int\frac{du}{dx}dx$
2) $EV=log_2\frac{L\cdot S}{K}$
3) $n^{(p_2)}$
4) $\frac{317\cdot4+2}{\frac{\sqrt{289}}{442}+314}$
5) $\binom{n}{d}$
6) $x_i=l_i,F_i(x)\geq0$ | u=\int\frac{du}{dx}dx
EV=log_2\frac{L\cdot S}{K}
n^{(p_2)}
\frac{317\cdot4+2}{\frac{\sqrt{289}}{442}+314}
\binom{n}{d}
x_i=l_i,F_i(x)\geq0 | [
{
"order": 1,
"latex": "u=\\int\\frac{du}{dx}dx",
"bbox": [
94,
51,
266,
139
]
},
{
"order": 2,
"latex": "EV=log_2\\frac{L\\cdot S}{K}",
"bbox": [
94,
163,
857,
407
]
},
{
"order": 3,
"latex": "n^{(p_2)}",
"bbox": [
... | |
021263 | human | handwriting | stack | photo | lines | 6 | 1,000 | 1,172 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\vec{r}=\begin{bmatrix}1\\0\end{bmatrix}$
$\hat{\theta}\in\Theta$
$x_2(t)=\dot{x_1}(t)$
$\frac{42}{1}\cdot\frac{36}{245}/2$
$\binom{t}{k}$
$x=\frac{-1}{y}+C$ | \vec{r}=\begin{bmatrix}1\\0\end{bmatrix}
\hat{\theta}\in\Theta
x_2(t)=\dot{x_1}(t)
\frac{42}{1}\cdot\frac{36}{245}/2
\binom{t}{k}
x=\frac{-1}{y}+C | [
{
"order": 1,
"latex": "\\vec{r}=\\begin{bmatrix}1\\\\0\\end{bmatrix}",
"bbox": [
48,
46,
216,
142
]
},
{
"order": 2,
"latex": "\\hat{\\theta}\\in\\Theta",
"bbox": [
48,
195,
446,
397
]
},
{
"order": 3,
"latex": "x_2(t)=... | |
058670 | human | handwriting | grid | photo | grid | 7 | 1,000 | 513 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\mu=\frac{1}{n}\sum_{i=1}^nx_i$
$\frac{d^2s}{dt^2}=-k^2s$
$\tilde{s}_i$
${\xi^{\delta}}^5$
$x^2/a^2+y^2/b^2=1$
$J_{-}|j-j\rangle=0$
$\frac{\frac{\frac{10}{383}}{\sqrt{6}}}{185+191}$ | \mu=\frac{1}{n}\sum_{i=1}^nx_i
\frac{d^2s}{dt^2}=-k^2s
\tilde{s}_i
{\xi^{\delta}}^5
x^2/a^2+y^2/b^2=1
J_{-}|j-j\rangle=0
\frac{\frac{\frac{10}{383}}{\sqrt{6}}}{185+191} | [
{
"order": 1,
"latex": "\\mu=\\frac{1}{n}\\sum_{i=1}^nx_i",
"bbox": [
48,
51,
309,
162
]
},
{
"order": 2,
"latex": "\\frac{d^2s}{dt^2}=-k^2s",
"bbox": [
369,
52,
630,
172
]
},
{
"order": 3,
"latex": "\\tilde{s}_i",
"... | |
117173 | human | handwriting | numbered | photo | white | 7 | 1,000 | 1,201 | by the printed number, in ascending order (1), 2), 3), ...) | Transcribe every handwritten formula on this page into LaTeX. Read them by the printed number, in ascending order (1), 2), 3), ...). Keep each formula's printed number as "N)" and put one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | 1) $x=\frac{1}{sin\alpha}$
2) $p_{cv}(t)\propto e^{-i\Delta\epsilon t/\hbar}$
3) $\underline{Z}$
4) $0\notin S$
5) $P\frac{4}{n}\frac{2}{b}\frac{2}{m}$
6) $J=\begin{bmatrix}0&I\\-I&0\end{bmatrix}$
7) ${2^7}^9/1+23$ | x=\frac{1}{sin\alpha}
p_{cv}(t)\propto e^{-i\Delta\epsilon t/\hbar}
\underline{Z}
0\notin S
P\frac{4}{n}\frac{2}{b}\frac{2}{m}
J=\begin{bmatrix}0&I\\-I&0\end{bmatrix}
{2^7}^9/1+23 | [
{
"order": 1,
"latex": "x=\\frac{1}{sin\\alpha}",
"bbox": [
94,
48,
370,
163
]
},
{
"order": 2,
"latex": "p_{cv}(t)\\propto e^{-i\\Delta\\epsilon t/\\hbar}",
"bbox": [
94,
200,
448,
301
]
},
{
"order": 3,
"latex": "\\und... | |
003183 | human | handwriting | grid | photo | white | 7 | 1,000 | 605 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{329}{139}+\frac{71}{1}$
$(|f|)$
$\sum_{i\in I}m_i\leq\sum_{i\in I}n_i$
$\hat{S}(n)$
$\int sin^mxcos^nxdx$
$h_9^{h_2^{h_3^{-^{-^{-}}}}}$
$\frac{5}{\sqrt{59}}\cdot(4-42)\cdot115$ | \frac{329}{139}+\frac{71}{1}
(|f|)
\sum_{i\in I}m_i\leq\sum_{i\in I}n_i
\hat{S}(n)
\int sin^mxcos^nxdx
h_9^{h_2^{h_3^{-^{-^{-}}}}}
\frac{5}{\sqrt{59}}\cdot(4-42)\cdot115 | [
{
"order": 1,
"latex": "\\frac{329}{139}+\\frac{71}{1}",
"bbox": [
48,
44,
309,
183
]
},
{
"order": 2,
"latex": "(|f|)",
"bbox": [
369,
46,
444,
98
]
},
{
"order": 3,
"latex": "\\sum_{i\\in I}m_i\\leq\\sum_{i\\in I}n_i",... | |
140035 | human | handwriting | twocol | photo | white | 11 | 1,000 | 927 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $a^{\prime}\in A$
$s_i\notin T$
$Q(x)=\prod_{n\geq1}(1-x^n)$
$\begin{bmatrix}1\\0\end{bmatrix}$
$0<\kappa<1/\sqrt{2}$
$A=T(V)/R$
$\frac{a-\lambda_{\pm}}{c}=\frac{c}{b-\lambda_{\pm}}$
$\int VdP$
$Z=n_i\times[Z]_i$
${36^{243}}^{\frac{7}{5}+244}$
$e_1,...,e_n$ | a^{\prime}\in A
s_i\notin T
Q(x)=\prod_{n\geq1}(1-x^n)
\begin{bmatrix}1\\0\end{bmatrix}
0<\kappa<1/\sqrt{2}
A=T(V)/R
\frac{a-\lambda_{\pm}}{c}=\frac{c}{b-\lambda_{\pm}}
\int VdP
Z=n_i\times[Z]_i
{36^{243}}^{\frac{7}{5}+244}
e_1,...,e_n | [
{
"order": 1,
"latex": "a^{\\prime}\\in A",
"bbox": [
48,
46,
363,
167
]
},
{
"order": 2,
"latex": "s_i\\notin T",
"bbox": [
48,
194,
435,
332
]
},
{
"order": 3,
"latex": "Q(x)=\\prod_{n\\geq1}(1-x^n)",
"bbox": [
... | |
060529 | human | handwriting | twocol | photo | white | 8 | 1,000 | 906 | down the LEFT column first, then down the RIGHT column | Transcribe every handwritten formula on this page into LaTeX. Read them down the LEFT column first, then down the RIGHT column. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $S$
$\hat{X}_q$
$\frac{a+b^n}{n}=x$
$\hat{\xi}$
$[-\infty,1/y_1]$
${{\sqrt{186}^{188}}^{10}}^{287-7}$
$s\begin{Bmatrix}7\\4\end{Bmatrix}$
$v=\sqrt{\frac{ke^2}{mr}}$ | S
\hat{X}_q
\frac{a+b^n}{n}=x
\hat{\xi}
[-\infty,1/y_1]
{{\sqrt{186}^{188}}^{10}}^{287-7}
s\begin{Bmatrix}7\\4\end{Bmatrix}
v=\sqrt{\frac{ke^2}{mr}} | [
{
"order": 1,
"latex": "S",
"bbox": [
48,
46,
107,
175
]
},
{
"order": 2,
"latex": "\\hat{X}_q",
"bbox": [
48,
219,
124,
375
]
},
{
"order": 3,
"latex": "\\frac{a+b^n}{n}=x",
"bbox": [
48,
422,
206,... | |
060843 | human | handwriting | stack | photo | white | 4 | 1,000 | 760 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{mv^2}{2}=\Delta E_{fly}$
$0^{0^{0^{.^{.^n}}}}$
$2^{2^{2^{2^{43}}}}$
$\sqrt{3}\approx1.73$ | \frac{mv^2}{2}=\Delta E_{fly}
0^{0^{0^{.^{.^n}}}}
2^{2^{2^{2^{43}}}}
\sqrt{3}\approx1.73 | [
{
"order": 1,
"latex": "\\frac{mv^2}{2}=\\Delta E_{fly}",
"bbox": [
48,
45,
255,
117
]
},
{
"order": 2,
"latex": "0^{0^{0^{.^{.^n}}}}",
"bbox": [
48,
166,
155,
249
]
},
{
"order": 3,
"latex": "2^{2^{2^{2^{43}}}}",
"b... | |
062779 | human | handwriting | stack | photo | white | 4 | 1,000 | 803 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\frac{\frac{8}{4}}{101-3}$
$P=\frac{m_7v}{\sqrt{8\cdot\frac{v^2}{x^2}}}$
$(\frac{10}{5}+\frac{284}{52})$
$\frac{1}{\gamma}=\sqrt{1-(v/c)^2}$ | \frac{\frac{8}{4}}{101-3}
P=\frac{m_7v}{\sqrt{8\cdot\frac{v^2}{x^2}}}
(\frac{10}{5}+\frac{284}{52})
\frac{1}{\gamma}=\sqrt{1-(v/c)^2} | [
{
"order": 1,
"latex": "\\frac{\\frac{8}{4}}{101-3}",
"bbox": [
48,
45,
415,
277
]
},
{
"order": 2,
"latex": "P=\\frac{m_7v}{\\sqrt{8\\cdot\\frac{v^2}{x^2}}}",
"bbox": [
48,
305,
159,
380
]
},
{
"order": 3,
"latex": "(\\... | |
170443 | human | handwriting | stack | photo | white | 6 | 1,000 | 1,308 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\binom{2n}{n}:=\frac{(2n)!}{(n!)^2}$
$|x^{\rho}|=\sqrt{x}$
${\sqrt{6}+333^{10}}^{{9^{140}}^{10}}$
$k_a=\frac{2\pi a}{\lambda}$
$\frac{d^kf}{dx^k}(x)=0$
$\frac{(\frac{7}{51}\cdot3)}{464-480^{\sqrt{86}}}$ | \binom{2n}{n}:=\frac{(2n)!}{(n!)^2}
|x^{\rho}|=\sqrt{x}
{\sqrt{6}+333^{10}}^{{9^{140}}^{10}}
k_a=\frac{2\pi a}{\lambda}
\frac{d^kf}{dx^k}(x)=0
\frac{(\frac{7}{51}\cdot3)}{464-480^{\sqrt{86}}} | [
{
"order": 1,
"latex": "\\binom{2n}{n}:=\\frac{(2n)!}{(n!)^2}",
"bbox": [
48,
50,
628,
273
]
},
{
"order": 2,
"latex": "|x^{\\rho}|=\\sqrt{x}",
"bbox": [
48,
295,
697,
523
]
},
{
"order": 3,
"latex": "{\\sqrt{6}+333^{10}... | |
024763 | human | handwriting | grid | photo | grid | 6 | 1,000 | 427 | left to right within each row, then row by row top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them left to right within each row, then row by row top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $10^{11}=\frac{l}{10e-12}$
$\begin{pmatrix}S_{11}&S_{12}\\S_{21}&S_{22}\end{pmatrix}$
$\int_0^t$
$\hat{N_{k_l}}=b_{k_l}^{\dagger}b_{k_l}$
$\tilde{P}\equiv det(P)P^{-1}$
$r=g^ey^v(modp)$ | 10^{11}=\frac{l}{10e-12}
\begin{pmatrix}S_{11}&S_{12}\\S_{21}&S_{22}\end{pmatrix}
\int_0^t
\hat{N_{k_l}}=b_{k_l}^{\dagger}b_{k_l}
\tilde{P}\equiv det(P)P^{-1}
r=g^ey^v(modp) | [
{
"order": 1,
"latex": "10^{11}=\\frac{l}{10e-12}",
"bbox": [
48,
46,
176,
270
]
},
{
"order": 2,
"latex": "\\begin{pmatrix}S_{11}&S_{12}\\\\S_{21}&S_{22}\\end{pmatrix}",
"bbox": [
369,
44,
630,
184
]
},
{
"order": 3,
"l... | |
056328 | human | handwriting | stack | photo | white | 4 | 1,000 | 778 | top to bottom | Transcribe every handwritten formula on this page into LaTeX. Read them top to bottom. Output one formula per line. Wrap each formula's LaTeX in $ ... $ and output nothing else. | $\rho_r^{\pi}$
$\int_Xfd\mu$
$\partial_pH=\dot{q}$
$\frac{y}{x}=tan\theta$ | \rho_r^{\pi}
\int_Xfd\mu
\partial_pH=\dot{q}
\frac{y}{x}=tan\theta | [
{
"order": 1,
"latex": "\\rho_r^{\\pi}",
"bbox": [
48,
52,
237,
229
]
},
{
"order": 2,
"latex": "\\int_Xfd\\mu",
"bbox": [
48,
264,
429,
488
]
},
{
"order": 3,
"latex": "\\partial_pH=\\dot{q}",
"bbox": [
48,
... |
End of preview. Expand in Data Studio
MathWriting → VLM pages (500k)
Multi-formula handwriting "pages" composed from
MathWriting, for VLM
formula-transcription training. Each page carries a prompt stating the reading
order and an answer — the per-formula LaTeX in that order, in a finalized
render-preserving canon (latexnorm, KaTeX-validated 100%).
Pages are single-source: a page is entirely human ink or entirely synthetic ink, never mixed, so the handwriting style within a page is consistent the way a real sheet is. The dataset as a whole covers both distributions.
| config | pages | placements | distinct targets | reuse |
|---|---|---|---|---|
human |
200,000 | 1,292,526 | 52,892 | ×24.4 |
synthetic |
300,000 | 1,938,703 | 351,628 | ×5.5 |
from datasets import load_dataset
human = load_dataset("elejke/mathwriting-vlm-500k", "human", split="train")
synth = load_dataset("elejke/mathwriting-vlm-500k", "synthetic", split="train")
Splits are train / validation (2,000 held-out pages per config).
Columns
| column | type | meaning |
|---|---|---|
image |
Image |
the page — PNG for clean, JPEG for photo |
prompt |
string |
instruction stating this layout's reading order |
answer |
string |
the target: per-formula LaTeX in reading order, each wrapped in $…$, printed number kept as N) on numbered pages |
target_plain |
string |
same target without delimiters or numbering, for metrics |
formulas |
list<{order, latex, bbox}> |
per-formula LaTeX and its box on the page |
id, source, domain |
string |
page id, human/synthetic, handwriting |
layout, variant, background |
string |
numbered/grid/stack/twocol, clean/photo, paper style |
n_formulas, width, height |
int64 |
formula count and page size in px |
Coordinate caveat for photo pages
width/height and formulas[].bbox are recorded in the pre-augmentation
page frame. For variant: "photo" pages the augmentation pipeline (augraphy) adds
a border and a slight warp, so the delivered JPEG is about 2% larger than the
recorded size and the boxes are offset accordingly (~20% of pages in each config).
This does not affect prompt / answer / target_plain at all — it only matters
if you consume the boxes. variant: "clean" PNGs match the recorded size exactly.
Composition
Both configs share the same generator and differ only in the ink source.
- layouts —
numbered,stack,twocol,grid; each has its ownorder_specand matching prompt, so reading order is always stated explicitly. - backgrounds — plain, lined, squared paper.
- augmentation — 40% of pages are
photo(augraphy: shadows, warp, noise, JPEG artifacts), the rest arecleanPNGs. - density — 4–11 formulas per page (median 6).
- page height — human 262–1862 px (median 892), synthetic 252–1985 px (median 997).
Target format
The LaTeX canon was chosen from what real VLMs actually emit on these images, not by taste — benchmarked across Qwen3.6-27B, Qwen3.5-27B, gemma-4-31B-it, GigaChat-3.5-432B and Gemini 3.5 Flash. Consequences:
- inline
$…$delimiters,N)numbering preserved on numbered pages; \cdotrather than\timesfor multiplication dots;- binomials as
\binom{n}{k}, not(\begin{matrix}n\\k\end{matrix})— the MathWriting source labels use plain delimiters that render small while the ink shows big ones, so this is a faithfulness fix to the label, not a render-preserving rewrite; - delimited matrices normalized to
pmatrix/bmatrix/Bmatrix/vmatrix/Vmatrix.
Validation
Both configs pass the same gate before publication:
- every record: unique id, formula order
1..n, boxes inside the page,answer/target_plainreconstructible fromformulas, image present and openable; - KaTeX render-check on a sample of targets — 100% renderable in both configs;
- every parquet shard checked against the source
dataset.jsonlfield by field, with row counts reconciled to 200,000 / 300,000 exactly.
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