harryrobert/nav2tex-decoder-latex-pretrain huggingface dataset:
e^{2 ( x +{\frac{i}{2}}\overrightarrow{\partial}_{p})}\, K_{i \left( P - p \right)}( e^{x + X}) \, K_{i \left( P + p \right)}( e^{x - X}) = e^{2 x}\, K_{1 + i \left( P - p \right)}( e^{x + X}) \, K_{- 1 + i \left( P + p \right)}( e^{x - X}) \, \; .
\mathsf{R}_{\tau}= (-2a^2+2at_1+bc+\frac{t_2}{3})\frac{\partial}{\partial a}+(6a^2c-\frac{ct_2}{2}-3ab+3bt_1)\frac{\partial}{\partial b}& +(ac+ct_1-\frac{b}{2})\frac{\partial}{\partial c}+(t_1^2-\frac{t_2}{12})\frac{\partial}{\partial t_1}+ (4t_1t_2-6t_3)\frac{\partial}{\partial t_2}
\left( \begin{array}{c}{{\hat{{\bf b}}}}\\{{\hat{{\bf b}}^{\dagger}}}\\ \end{array}\right) = \Omega \left( \begin{array}{c}{{\hat{{\bf a}}}}\\{{\hat{{\bf a}}^{\dagger}}}\\ \end{array}\right) + \left( \begin{array}{c}{{{\bf d}}}\\{{{\bf d}^{*}}}\\ \end{array}\right) , \qquad \Omega = \left( \begin{array}{c c}{{\zeta}}&{{\eta}}\\{{\eta^{*}}}&{{\zeta^{*}}}\\ \end{array}\right) ,
\left. h_{a}^{( I )}\right.^{2}= \left. h_{b}^{( I )}\right.^{2}= \sigma^{( I )}, \qquad \mathrm{w h e r e}\qquad \sigma^{( I )}= \frac{1}{t^{( I )}d_{I}+ \left. \vec{\alpha}^{( I )}\right.^{2}/ 4}.
\varphi_m'(x) =-\widetilde{E}_m'(x) &=-\left(f_1'(x)+f_1(x)\sum_{k=0}^{m-1}\frac{x^k}{q^{k+1}-1}\right)\exp\left(\sum_{k=1}^{m}\frac{x^k}{k(q^k-1)}\right) &=-\left(\sum_{n\geq0}\frac{(n+1)x^n}{(q;q)_{n+1}}+\sum_{k=0}^{m-1}\left(\sum_{n\geq k}\frac{x^n}{(q^{k+1}-1)(q;q)_{n-k}}\right)\right)\exp\left(\sum_{k=1}^{m}\frac{x^k}{k(q^k-1)}\right).
|a_n'(\theta,x,y)|\leq\begin{cases}C n (\theta\in I_1), C (n^{-1}(\theta-(n-1)\pi)^{-2}+1) (\theta\in I_2), C (n^{-1/2}+1) (\theta\in I_3), C (n^{-1}(n\pi - \theta)^{-2}+1) (\theta\in I_4), C n (\theta\in I_5),\end{cases}
f^{L}(\vec x) =\int_0^{\|x\|_\infty}f(V_t^+(\vec x),V_t^-(\vec x))d t &=\int_0^{\|x\|_\infty}f(V_t^-(\vec x),V_t^+(\vec x))d t &=\int_0^{\|x\|_\infty}f(V_t^+(-\vec x),V_t^-(-\vec x))d t =f^{L}(-\vec x),
\frac{d}{dt}\left(\lambda(\widetilde{g}_i,\widetilde{H}_i)-\lambda(g_c,H_c) \right)^{1-2\alpha}=(1-2\alpha)\left(\lambda(\widetilde{g}_i,\widetilde{H}_i)-\lambda(g_c,H_c) \right)^{-2\alpha}\frac{d}{dt}\lambda(\widetilde{g}_i,\widetilde{H}_i) &\geq -C.
\int_0^1\int_0^1\partial_{y_i}f(s,t,Y_{s,t})\mathrm{d}t\mathrm{d}s = -\int_0^1\int_0^1f(s,t,Y_{s,t})\frac{\mathrm{d}_tY^{(i)}_{s,t}}{s}\mathrm{d}s-\int_0^1\int_{0}^1f(s,1-t,Y_{s,1-t})\frac{\mathrm{d}_tB^{(i)}_{s,t}}{s}\mathrm{d}s &+\int_0^1\int_{0}^1f(s,1-t,Y_{s,1-t})\frac{Y^{(i)}_{s,1-t}}{s(1-t)}\mathrm{d}t\mathrm{d}s,
I_{1 0 2}^{a b c}= \frac{2 g f_{a b c}}{( 2 \pi )^{4}x_{1 2}^{2}}\left[ [ 2 1^{-}] \rho_{1}^{2}+ [ 1 2^{-}] \rho_{2}^{2}- 2 ( \rho_{1}\rho_{2}) \right] \; .