Mathpix - Convert images to LaTe

2019-04-17  本文已影响0人  寂然不动

Mathpix
Mathpix examples

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  1. f(x)=\frac{1}{\sqrt{2 \pi \sigma x}} e^{-\frac{(x-\mu)^{2}}{2 \sigma^{2}}}

  2. \mathcal{L}(q)=E_{q(\tau)}[\log p(\tau)]+E_{q(\theta)}[\log p(\theta)]+E_{q(\mathbf{z}) q(\tau)}[\log p(\mathbf{z} | \tau)]

  3. H(Y | X)=\sum_{x \in \mathcal{X}, y \in \mathcal{Y}} p(x, y) \log \left(\frac{p(x)}{p(x, y)}\right)

  4. \left( \begin{array}{l}{c t^{\prime}} \\ {x^{\prime}} \\ {y^{\prime}} \\ {z^{\prime}}\end{array}\right)=\left( \begin{array}{cccc}{\gamma} & {-\gamma \beta} & {0} & {0} \\ {-\gamma \beta} & {\gamma} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {1}\end{array}\right) \left( \begin{array}{l}{c t} \\ {x} \\ {y} \\ {z}\end{array}\right)

  5. \delta B_{\mu \nu}^{p}=\mathcal{D}_{\mu}^{p q} \xi_{\nu}^{q}-\mathcal{D}_{\nu}^{p q} \xi_{\mu}^{q} \equiv R_{\mu \nu \alpha}^{p q} \xi^{q \alpha}, \delta A_{\mu}^{p}=0

  6. \Phi^{(I)}=-\frac{s e^{2} F(1-F)}{12 \pi^{2}|m|} \int_{1}^{\infty} \frac{d v}{v \sqrt{v-1}} \frac{(1+F)\left(1+A v^{F}\right)-(2-F)\left(1+A^{-1} v^{1-F}\right)}{A v^{F}+2+A^{-1} v^{1-F}}

  7. \Gamma_{\epsilon}(x)=\left[1-e^{-2 \pi \epsilon}\right]^{1-x} \prod_{n=0}^{\infty} \frac{1-\exp (-2 \pi \epsilon(n+1))}{1-\exp (-2 \pi \epsilon(x+n))}

  8. T_{x}\left(\theta_{r}\right)=\left[ \begin{array}{cccc}{1} & {0} & {0} & {0} \\ {0} & {\cos \theta_{r}} & {\sin \theta_{r}} & {0} \\ {0} & {-\sin \theta_{r}} & {\cos \theta_{r}} & {0} \\ {0} & {0} & {0} & {1}\end{array}\right]

  9. W_{b}^{*}=n\left(\hat{\theta}_{b}^{*}-\hat{\theta}\right)^{\prime} \hat{V}_{b}^{*}\left(\hat{\theta}_{b}^{*}-\hat{\beta}\right)

  10. T_{j, i}^{(t)} :=\mathrm{P}\left(Z_{i}=j | X_{i}=\mathbf{x}_{i} ; \theta^{(t)}\right)=\frac{\tau_{j}^{(t)} f\left(\mathbf{x}_{i} ; \boldsymbol{\mu}_{j}^{(t)}, \Sigma_{j}^{(t)}\right)}{\tau_{1}^{(t)} f\left(\mathbf{x}_{i} ; \boldsymbol{\mu}_{1}^{(t)}, \Sigma_{1}^{(t)}\right)+\tau_{2}^{(t)} f\left(\mathbf{x}_{i} ; \boldsymbol{\mu}_{2}^{(t)}, \Sigma_{2}^{(t)}\right)}

  11. \frac{\gamma}{4}\left(\frac{(D \Omega)^{2}}{\Omega^{2}}-2 \frac{D \cdot D \Omega}{\Omega}\right)+(1-\lambda) \mu \Omega^{-\lambda}-\frac{1}{4}\left(1-\frac{\epsilon}{2}\right) \Omega^{-\epsilon / 2} F^{2}=T_{\Omega}^{X}

  12. \left\langle v_{I, A \tilde{A}}(\tau) v_{J, B \tilde{B}}^{\dagger}\left(\tau^{\prime}\right)\right\rangle=\delta^{I J} \delta^{A B} \delta^{\tilde{A} \tilde{B}} \int \frac{d k}{2 \pi} \frac{e^{i k\left(\tau-\tau^{\prime}\right)}}{k^{2}+r^{2} / \lambda^{2}} \equiv \delta^{I J} \delta^{A B} \delta^{\tilde{A} \tilde{B}} \Delta\left(\tau-\tau^{\prime}\right)

  13. \Omega_{a \nu}(a z, b z)=\frac{\overline{K}_{\nu}^{(b)}(b z) / \overline{K}_{\nu}^{(a)}(a z)}{\overline{K}_{\nu}^{(a)}(a z) \overline{I}_{\nu}^{(b)}(b z)-\overline{K}_{\nu}^{(b)}(b z) \overline{I}_{\nu}^{(a)}(a z)}

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