Datasets:
prithivMLmods
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Latex-KIE

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\begin{align*} \frac 1{2\pi i}\int\limits_{c-i\infty }^{c+i\infty }ds\frac{(-s)}{\mu}\left(\frac{t}{\mu}\right)^{-s-1}\frac{2^{s-1}}{\sqrt{\pi}}\Gamma \left( \frac{ s+1}2\right) \left[ \mu^{-s}\Gamma \left(\frac s2\right) \zeta \left( \frac s2, \frac{D_B}{\mu ^2}\right)\right]\,,\end{align*}
\begin{align*}K\equiv\frac{p^{0}a^{1}-pa^{0}}{mc};\;\;\Lambda\equiv\sqrt{1-k({a^{0}}^{2}-{a^{1}}^{2})}\,,\end{align*}
\begin{align*}{\cal I}|_{j^a (j-1728)^b} \sim (T-\rho)^{2a - 2},\end{align*}
\begin{align*}ds^2 = (dT)^2 - R(T)^2 \sum_{i=1}^{D-1}(dX^i)^2\end{align*}
\begin{align*}F _2 (z) = \sum _{n=-\infty} ^{\infty} \frac{1}{1-4 n ^2} \frac{\coth \left( \frac{\sqrt{4 \pi ^2 n ^2 + z ^2}}{2} \right)}{\sqrt{4 \pi ^2 n ^2 + z ^2}}\end{align*}
\begin{align*}A_l(N,k) = \sum_{p=1}^{k-1}(-1)^{k-p-1}(k-p)^{l-1}\left(\begin{array}{c}N \\p\end{array}\right) \end{align*}
\begin{align*}{\cal L}_{\rm bulk}(t,y)={M_3^2\over 2} \sqrt g\ \left(R-\frac{1}{2}(\partial\phi)^2-{3\over 2}\frac{e^{2\phi}{\cal F}^2}{5!}\right) = -{3 M_3^2 \tilde {A}^3 B\over \tilde N} \left [\left({\dot {\tilde A} \over \tilde A}\right)^2 -{7 \over 4} \left({\dot D\over D}\right)^2 \right].\end{align*}
\begin{align*}\langle Z_1 \, Z_2 , P \rangle = \langle Z_1 \otimes Z_2 , \Delta \, P \rangle \, . \end{align*}
\begin{align*}\widetilde{\phi}_j(x)= \widehat{\phi}_j(x+\frac{n}{m}j).\end{align*}
\begin{align*}\Pi^{\underline{m}}_{+q} = 0\end{align*}
\begin{align*}\int {\cal D}[\overline \Psi, \Psi, A] \> {\cal O}[\overline \Psi, \Psi, A] \>e^{-S_{\rm QCD}[\overline \Psi, \Psi, A]}\;\;\;.\end{align*}
\begin{align*}R_{11',22',33'}(u,v,w)\ =\ R_{12}(v,w)\ R_{1'3}(u,w)\ R_{2'3'}(u,v)\end{align*}
\begin{align*}ds^2=-e^{2A(r)}dt^2+e^{2B(r)}[dr^2+r^2d\Omega_n^2]+\sum_a e^{2C_a(r)}dy_a^2.\end{align*}
\begin{align*}\Lambda^{(1)} = \lambda^{(1)} + \theta A + q \theta^2 \lambda^{(2)},\end{align*}
\begin{align*}\lbrack -i\rho_2{d\over dr} +\rho_1(W+{\kappa\over r})-E+V+M\rho_3\rbrack\Phi=0\end{align*}
\begin{align*}R^{(\pm)}_N(\nu,k)=\int_{1}^{\infty}d\alpha(\sum_{\ell=1}^{2N+3}\frac{\Phi^{(N+1)}_{\ell}(\alpha)}{(\alpha\pm ik)^{\ell})}[\alpha^{\nu/2}+\alpha^{-\nu/2}],\end{align*}
\begin{align*}\int [dg] \psi^{\dagger}(g)\psi(g)~=~1 \; .\end{align*}
\begin{align*}Z_{(m) A} ^{\ I} = \int _{S^{p+2}} L_\Lambda^{\ I} F^\Lambda = L_\Lambda^{\ I} (\phi_0) g^\Lambda\end{align*}
\begin{align*}I_{ct(AdS)} = \frac{2}{\ell}\frac{1}{8\pi}\int_{\partial M_\infty} d^{3}x\sqrt{\gamma}\left(A + B\frac{\ell^2}{4} R(\gamma)\right)\end{align*}
\begin{align*}B^2 =C'^2-F'A'=\left(C'-\frac{C}{A}A' \right)^2.\end{align*}
\begin{align*}\left\{ Q_\alpha ,\bar{Q}_{\dot{\beta}}\right\} =\sigma _{\alpha \dot{\beta}}^\mu \,p_\mu \,\,,\end{align*}
\begin{align*}\chi_c \:C\:i^{|I_1|+\cdots+|I_k|} \:(-i)^{|K|} \;\gamma^I\;(\partial^{I_k} V^{(k)}_{J_k, c_k}(x)) \cdots(\partial^{I_1} V^{(1)}_{J_1, c_1}(x))\:(y-x)^K \;S^{\vee (h)}(x,y) \;\;\; , \end{align*}
\begin{align*}\pi_{i}= \frac{\partial\mathcal{L}}{\partial \dot{x}^{i}} = g_{ij}\dot{x}^{j} + B_{ij}x'^{j}\;, \end{align*}
\begin{align*}V_B=- m^{\delta} \phi^{\gamma} + {\rm H.c.} \ ,\end{align*}
\begin{align*}\displaystyle\frac{{\cal J}_-}{{\cal J}_+} = 2 \displaystyle\frac{J_{l - \xi}(ka)J_{l + \Phi} (ka) - J_l(ka) J_{l + \Phi - \xi} (ka)}{J_{l - \xi}(ka) H^+_{l + \Phi} (ka) - J_l (ka) H^+_{l + \Phi - \xi} (ka)} -1.\end{align*}
\begin{align*}H_a=-2 A(\lambda_a) \pi_a^2-\frac{1}{2} \left[\lambda_a^2(\lambda_a-\bar{\sigma}_2^2)(\lambda_a-\bar{\sigma}_3^2)\right]\end{align*}
\begin{align*}\tilde T^{x}_{_{(0)}x} = c[\varphi'^2 +\end{align*}
\begin{align*}\sigma'^2 + \left(\frac{A'}{e}\right)^2 + \alpha \Lambda'^2] + s\frac{\varphi^2P^2}{r^2} +\end{align*}
\begin{align*}\frac{1}{2}\left(\frac{P'}{qr}\right)^2 -\frac{1}{2} \sigma^2 A^2 -\end{align*}
\begin{align*}\tilde T^{y}_{_{(0)}y} = s [\varphi'^2 +\end{align*}
\begin{align*}\sigma'^2 + \left(\frac{A'}{e}\right)^2 + \alpha \Lambda'^2] + c\frac{\varphi^2 P^2}{r^2} +\end{align*}
\begin{align*}\frac{1}{2}\left(\frac{P'}{q r}\right)^2 - \frac{1}{2}\sigma^2 A^2\end{align*}
\begin{align*}- 2V, \end{align*}
\begin{align*}x_{+}=F_{0}(\zeta)+\frac{1}{n-2} \sum_{\kappa=1}^{n-3} \mu_{\kappa}(-p)^{\kappa} F_{\kappa}(\zeta)\end{align*}
\begin{align*}d{\hat s}^{2}={\hat g}_{MN}(x)dx^{M}dx^{N}\end{align*}
\begin{align*}\chi_y(E)_{\rm LG}=\sum_{l=0}^D(-y)^l\sum_{s=0}^r(-1)^s\dim{\cal H}^{l}(X,\wedge^{s}E)\,,\end{align*}
\begin{align*}\rho_{\pm} = \frac{(1+\alpha^2) (M \pm \sqrt{ M^{2} - \left( 1-\alpha^{2} \right) Q^{2}})}{\left(1 \pm \alpha^{2}\right)}, \; \; \; a = \frac{2 (1 + \alpha^2) J}{ (1 + \alpha^2) \rho_{+} +(1-\alpha^{2}/3) \rho_{-}} . \end{align*}
\begin{align*}A_{2}=\sum_{k=0}^{2}{\Omega_{k}(t)\over (f_{\theta}(t))^{k}},\end{align*}
\begin{align*}\left( \partial_r +\frac 1r \right) \partial_r \sigma =\left[ -\Delta_w \sigma \right] +\left[ - \frac 1{r^2}\partial_\theta^2 + 2\phi\phi^* \right]\sigma\,,\end{align*}
\begin{align*}\epsilon^{0} \; : \; W_{0\eta\overline{\eta}}={k\over 2}e^{W_0}\end{align*}
\begin{align*}W=\xi\left[\zeta\phi-{1\over 3}\zeta^3\phi^3-{2\over 3}\right]~,\end{align*}
\begin{align*}\omega(x-y) = \arctan \left( \frac{x^2 - y^2}{x^1 - y^1} \right)\end{align*}
\begin{align*}\Delta n_\sigma = 3 - 2\sqrt{3}|\cos\xi_*|\end{align*}
\begin{align*}\delta {\cal E}_H=T_H \delta S^{BH}+\Phi \delta q~~~,\end{align*}
\begin{align*}\int d^{p+1} x \sqrt{g^i _{\mbox{\scriptsize brane}}} \equiv\int d^{p+1} x e^{-\phi + \phi_0}\sqrt{g^i _{\mbox{\scriptsize string}}}\end{align*}
\begin{align*}X(\sigma,0) = x + i\sqrt{\frac{\alpha'}{2} } \sum_{ { m={-\infty} }\atop {m \neq 0} }^\infty\frac{\alpha_m}{m} ( e^{im\sigma} \pm e^{-im\sigma} )\end{align*}
\begin{align*}\langle \psi|\alpha(x)\bar{\Gamma}|\psi \rangle=\int (dx) \alpha(x)\psi^{\dagger}(x)\bar{\Gamma}\psi(x).\end{align*}
\begin{align*}F_1(z)=z^{\nu +m+1}\frac{J_\sigma (a\sqrt{z^2+z_1^2})}{\left( z^2+z_1^2\right) ^{\sigma /2}}, \quad a>0\end{align*}
\begin{align*}E_{i} = \partial_{0}A_{i} - \partial_{i}A_{0} + i[A_{0}, A_{i}] = 0\end{align*}
\begin{align*}{\cal L}^{(1)} = { \frac{1} {2}}{\epsilon^{jki}\partial_j{A_k}^{a}}{\epsilon_{ab}\partial_{0}{A^b_{i}}}- {\frac{1}{4}}{F^{a,jk}}{{F^a}_{jk}} +{\dot \lambda^{(a)}}{A^{a}_3}\end{align*}
\begin{align*}E = {M(\rho) \cosh^2 \! \rho \over \sqrt{\cosh^2 \! \rho - {\dot\rho}^2}} - {2\pi q L T_{\rm F}} \sinh^2\! \rho\, ,\end{align*}
\begin{align*}\frac{\mbox{Area}_H}{4 \pi} \, = \, \sum_{i=1}^{p} \vert \, Z_i^{fix} \,\vert^2\end{align*}
\begin{align*}G\left( x,y\right) =\left( D_{\mu }D^{\mu }+m^{2}\right) ^{-1}\delta^{4}\left( x-y\right) \end{align*}
\begin{align*}\sin\left[2\eta_{\pm m\kappa}\left(0\right)\right]=0\end{align*}
\begin{align*}(G^{-1}_{OM})_{ab} = {\left( (2K^2 -1) - 2K^2 \sqrt{1-K^{-2}} \right)^{1\over6} \over K} \, \left[ \hat{\eta}_{\hat{a}\hat{b}} + \, {1\over 4} (\hat{{\cal H}}^2)_{\hat{a}\hat{b}} \right]\end{align*}
\begin{align*}\xi ^{\ast 2}=\frac{1}{2}\,\xi ^{2}-\frac{c}{eB}\,\xi ^{3} \end{align*}
\begin{align*}K_{nm}([x], \tau) = i g_{nm} \dot{x}(t') e^{i(\Omega_n - \Omega_m)t'}\end{align*}