软协论坛现已支持 LaTeX 公式渲染

即日起,你可以在本站使用 LaTeX 公式,所有公式将由 Mathjax 渲染。

行内公式添加示例:

$\hat{H}\Psi=E\Psi$

效果如下: \hat{H}\Psi=E\Psi

块级公式添加示例:

$$
\hat{H}\Psi=E\Psi
$$

效果如下:

\hat{H}\Psi=E\Psi

试试效果如何: -)

\begin{aligned} \sum_{x^\frac{1}{10} < r \leq x^{\frac{1}{3}}} P_{x} (x , p , x^{\frac {1} {10}}) &\leq\left\{\frac {20 (1 + \sqrt {e}) e^{- r} x C_{r}} {(\log x)^{2}} \right\} \left\{\sum_{x^\frac{1}{10} < r \leq x^{\frac{1}{5}}}\left(\frac {2 c^{r}} {p}\right)\cdot \left(1 + \int_{2}^{4 - \frac {100 \log p} {\log x}} \frac {\log (t - 1)} {t} \mathrm{d}t\right)\left(\frac {\log x^{\frac {1} {10}}} {\log \frac {x^{\frac {1} {2}}} {p}}\right)+\sum_{x^\frac{1}{5} < r \leq x^{\frac{1}{3}}}\frac {2 e^{r} \log x^{\frac {1} {10}}} {p \log \frac {x^{\frac {1} {2}}} {p}}\right\}\\ &\leq\left\{\frac {(4 + 5 \sqrt {e}) x C_{x}} {\log x} \right\} \left\{\int_{x^\frac{1}{10}}^{x^\frac{1}{5}}\frac {\mathrm{d} S} {S (\log S) (\log \frac {x^{\frac {1} {2}}} {S})}\int_{2}^{4 - \frac {10 \log s} {\log x}} \frac {\log (t - 1)} {t} \mathrm{d} t+ \int_{x^{\frac {1} {2}}}^{x^{\frac {1} {3}}} \cdot \frac {d S} {S (\log S) (\log \frac {x^{\frac {1} {2}}} {S})}\right\}\\ &=\left\{\frac {(4 + 5 \sqrt {e}) x C_{x}} {\log x} \right\} \left\{\int_{\frac {1} {10}}^{\frac {1} {5}} \frac {d \alpha} {u (\frac {1} {2} - \alpha)} \int_{2}^{t - 10 a} \frac {\log (t - 1)} {t} \mathrm{d} t+\int_{\frac {1} {10}}^{\frac {2} {3}} \frac {d \alpha} {\alpha (\frac {1} {2} - \alpha)}\right\}\\ &=\left\{\frac {(8 + 10 \sqrt {e}) x C_{x}} {\log x} \right\} \left\{\log 8 + \int_{\frac {1} {10}}^{\frac {1} {5}} \frac {d \alpha} {2 \pi (\frac {1} {2} - \alpha)} \int_{2}^{4 - 10 a} \frac {\log (t - 1)} {t} d t \right\} \end{aligned}

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