image imagewidth (px) 65 845 | latex_formula stringlengths 6 152 |
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\[\log(z \log z)\] | |
\[\sum_{k}f_{k}= \sum_{k}h_{k}=1\] | |
\[h_{xx}=-h_{yy} \neq 0\] | |
\[6 \sqrt{3}\] | |
\[-4( \gamma+ \log 4)+b+ \frac{4B \pi^{2} \sqrt{1-x}}{ \sqrt{1+3x}}\] | |
\[x^{3}x^{4}x^{5}\] | |
\[zy^{2}=4x^{3}-g_{2}z^{2}x-g_{3}z^{3}\] | |
\[2a_{1}+2a_{2}+2a_{3}+2a_{4}+2a_{5}+2a_{6}\] | |
\[k_{a} \neq k_{b} \neq k_{c}\] | |
\[1- \sum \alpha_{i}\] | |
\[AA\] | |
\[F=c+ \alpha x^{2}+ \beta y^{2}+ \gamma x^{2}y^{2}\] | |
\[x^{3}x^{4}x^{5}\] | |
\[\frac{i}{k+i}=1- \frac{k}{k+i}\] | |
\[y \geq 0\] | |
\[b_{n}= \lim_{ \alpha \rightarrow 0}b_{n- \alpha}\] | |
\[a= \sqrt{ \frac{5}{6}}\] | |
\[\frac{+1}{ \sqrt{2}}\] | |
\[\frac{x_{n}^{i}}{y_{n}^{b}}\] | |
\[foranyroot\] | |
\[(001000000)\] | |
\[\sqrt{mn}\] | |
\[\frac{25}{96} \frac{ \sqrt{ \pi}}{R^{3}}\] | |
\[r_{c}= \sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}\] | |
\[P= \int dz \sqrt{G_{ij}d \phi^{i}/dzd \phi^{j}/dz}\] | |
\[\frac{1}{3!1!}\] | |
\[\cos(zv)/ \sin(z)\] | |
\[X_{9}(X_{2}X_{7}-X_{3}X_{6})\] | |
\[2 \pi( \sin \theta_{1}+ \sin \theta_{2})\] | |
\[x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=1\] | |
\[\alpha \rightarrow \frac{ \alpha}{2} \sqrt{ \frac{5}{3}}\] | |
\[\int d^{d}x \sqrt{g}\] | |
\[g_{n}(x)=a_{n}x^{2}+b_{n}x+c_{n}\] | |
\[\frac{1}{ \sqrt{2}}\] | |
\[M \rightarrow \frac{M}{ \sqrt{c}}\] | |
\[H_{aa}=H_{xx}+H_{yy}\] | |
\[a(t)= \sin(Ht)\] | |
\[(2.4.9)-(2.4.10)\] | |
\[x^{2}+y^{2}+z^{k+1}\] | |
\[\int x^{m}(a+bx^{n})^{p}dx\] | |
\[56_{c}+8_{v}+56_{v}+8_{c}\] | |
\[\tan( \theta/2) \sin^{2}( \theta/2)\] | |
\[- \frac{1}{24}+ \frac{1}{16}= \frac{1}{48}\] | |
\[\sum_{i}b^{i}(x_{1}-x_{2})^{i}=0\] | |
\[\sqrt{1+z^{2}}\] | |
\[x=a(t-t_{0})^{-1}+p(t-t_{0})^{r-1}\] | |
\[\frac{6}{ \sqrt{60}}\] | |
\[\frac{n}{2}+ \frac{5}{2}\] | |
\[(n+1) \times(n+1) \times \ldots \times(n+1)\] | |
\[1+ \sqrt{1+m^{2}+q^{2}}\] | |
\[x_{k+1}x_{k}-x_{k}x_{k+1}=0\] | |
\[x^{4}-x^{5}\] | |
\[f^{-1}f=ff^{-1}=1\] | |
\[X=L \cos(s) \cos(t)\] | |
\[\frac{1}{2} \leq x \leq \frac{3}{2}\] | |
\[C= \frac{1}{32}+ \frac{1}{96} \log 2\] | |
\[x=- \log(1-y)\] | |
\[0=e^{-u}+e^{u-v-t}+e^{-v}+1\] | |
\[a=4( \frac{1}{4}- \frac{3}{8})\] | |
\[\sin^{2}F\] | |
\[\beta= \sqrt{1+b}\] | |
\[F(X)= \sqrt[3]{1+X}\] | |
\[z= \frac{1}{ \sqrt{2}}(x^{1}+ix^{2})\] | |
\[(a-b)-(k-b-c) \times(a-b)=(a-k+c) \times(a-b)\] | |
\[\frac{n}{ \sqrt{a_{1}b_{1}}} \leq 1\] | |
\[1 \ldots k\] | |
\[(x,y)=M( \cos( \alpha), \sin( \alpha))\] | |
\[x \frac{P(-x)}{(xP(x))^{2}}\] | |
\[2 \pi \sin \alpha\] | |
\[3 \times 3 \times 3+10 \times 3+3\] | |
\[24-4-2(3+3+2)=4\] | |
\[\frac{777}{400}\] | |
\[\sin^{2} \theta \leq 1\] | |
\[3 \times 3+r-3\] | |
\[z \geq \frac{9}{8}\] | |
\[\frac{ \pi}{2}+n \pi\] | |
\[n \times n\] | |
\[2f-e_{1}-e_{3}+2e_{6}+e_{7}+2e_{9}\] | |
\[[ab]=ab-ba\] | |
\[\frac{(2n-2)(2n-2)}{n-1}+4=4n\] | |
\[\frac{d}{dy}(y \frac{dw}{dy})-2w(w^{2}-1)=0\] | |
\[(x^{1})^{2}+(x^{2})^{2}+ \ldots+(x^{n+1})^{2}=1\] | |
\[\sin(kr)\] | |
\[\lim_{z \rightarrow \infty}zs(z)< \infty\] | |
\[[3][3][4]\] | |
\[\sum q_{i}=- \frac{1}{4}\] | |
\[\sin( \pi x)\] | |
\[T= \lim_{u \rightarrow \infty}uz\] | |
\[e^{-iu/2}(a_{1}+ia_{2})=x_{1}+ix_{2}=e^{iu/2}(b_{1}+ib_{2})\] | |
\[c \rightarrow c+da\] | |
\[x^{4} \ldots x^{9}\] | |
\[\int c_{z}\] | |
\[-2x^{-1}+ \frac{1}{2}(1+x^{-2})=0\] | |
\[2 \sin^{2} \alpha=1- \cos 2 \alpha\] | |
\[ap= \sin(aE)v\] | |
\[n+7\] | |
\[\sqrt{-M}\] | |
\[E^{ \prime}=E_{1}+E_{2}-E_{3}\] | |
\[A_{i}\] | |
\[\frac{-4}{ \sqrt{360}}\] |
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