![在对齐环境内,拆分方括号内的两行方程](https://linux22.com/image/442374/%E5%9C%A8%E5%AF%B9%E9%BD%90%E7%8E%AF%E5%A2%83%E5%86%85%EF%BC%8C%E6%8B%86%E5%88%86%E6%96%B9%E6%8B%AC%E5%8F%B7%E5%86%85%E7%9A%84%E4%B8%A4%E8%A1%8C%E6%96%B9%E7%A8%8B.png)
我有以下等式:
\begin{align}
\left[
1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{m \, t}{\sigma \, \sqrt{n}} - \frac{m^2 \, t^2}{\sigma^2 \, n} + \frac{1}{2} \frac{m^3 \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} -
\frac{\mathbb{E} [X_1^2]}{2} \frac{m \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{4} \frac{m^2 \, t^4}{\sigma^4 \, n^2} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n
\end{align}
我想通过使用\\
例如来拆分它,但是出现错误:
\begin{align}
\left[
1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{m \, t}{\sigma \, \sqrt{n}} - \frac{m^2 \, t^2}{\sigma^2 \, n} + \frac{1}{2} \frac{m^3 \, t^3}{\sigma^3 \, n^{3/2}} +
\\
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} -
\frac{\mathbb{E} [X_1^2]}{2} \frac{m \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{4} \frac{m^2 \, t^4}{\sigma^4 \, n^2} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n
\end{align}
编辑
\begin{align}
...
&= \Bigg\{ \Bigg\{ 1 + m \, \frac{t}{\sigma \, \sqrt{n}} + \mathbb{E} [X_1^2] \, \frac{1}{2} \left(\frac{t}{\sigma \, \sqrt{n}}\right)^2 + O\left[ \left( \frac{t}{\sigma \, \sqrt{n}} \right)^3 \right] \Bigg\}
\\
&\Bigg\{ 1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \left( \frac{m \, t}{\sigma \, \sqrt{n}} \right)^2 + O\left[ \left( \frac{m \, t}{\sigma \, \sqrt{n}} \right)^3 \right] \Bigg\} \Bigg\}^n = \\
&=
\left[
1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{m \, t}{\sigma \, \sqrt{n}} - \frac{m^2 \, t^2}{\sigma^2 \, n} + \frac{1}{2} \frac{m^3 \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} -
\frac{\mathbb{E} [X_1^2]}{2} \frac{m \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{4} \frac{m^2 \, t^4}{\sigma^4 \, n^2} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n
= \\
&= \left[
1 - \cancel{\frac{m \, t}{\sigma \, \sqrt{n}}} +
\frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\cancel{\frac{m \, t}{\sigma \, \sqrt{n}}} -
\frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n = \\
&=
\left[
1 - \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n = \\
&=
\left[
1 +
\left( \mathbb{E} [X_1^2] - m^2 \right)
\, \frac{t^2}{2 \, \sigma^2 \, n} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n =
&& \text{(g)} \\
&=
\left[
1 + \sigma^2 \frac{t^2}{2 \, \sigma^2 \, n} + O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n = \\
&=
\left[ 1 + \frac{t^2}{2 \, n} + O \left( \frac{t^3}{n^{3/2}} \right) \right]^n
\end{align}
答案1
像这样?
对于这个align
环境来说,这不是正确的选择。相反,你应该alined
在某些数学环境中使用它(例如equation
或\[ ... \]
),或者像我在以下 MWE 中所做的那样:使用包multiline
中定义的环境mathtools
。
\documentclass{article}
\usepackage{amssymb, mathtools}
\begin{document}
\[
\left[
\begin{multlined}
1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{m \, t}{\sigma \, \sqrt{n}} - \frac{m^2 \, t^2}{\sigma^2 \, n} + \frac{1}{2} \frac{m^3 \, t^3}{\sigma^3 \, n^{3/2}} +
\\
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} -
\frac{\mathbb{E} [X_1^2]}{2} \frac{m \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{4} \frac{m^2 \, t^4}{\sigma^4 \, n^2} +
O \left( \frac{t^3}{n^{3/2}} \right)
\end{multlined}
\right]^n
\]
\end{document}
附录
关于您的评论:如果您出于某种(未知的)原因坚持使用align
环境,则您无法在整个方程组周围获得括号,而只能在第一行的开始和第二行的结束处获得括号:
\documentclass{article}
\usepackage{amssymb, amsmath}
\begin{document}
\begin{align*}
& \left[
1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{m \, t}{\sigma \, \sqrt{n}} - \frac{m^2 \, t^2}{\sigma^2 \, n} + \frac{1}{2} \frac{m^3 \, t^3}{\sigma^3 \, n^{3/2}} + \right.
\\
&\ \left.\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} -
\frac{\mathbb{E} [X_1^2]}{2} \frac{m \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{4} \frac{m^2 \, t^4}{\sigma^4 \, n^2} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n
\end{align*}
\end{document}
据我理解,你的问题在于第一种可能性。
答案2
您可以\left[
用\right.
和\right]
来平衡\left.
,但不能保证括号的大小相同。
\documentclass{article}
\usepackage{amsmath, amssymb}
\begin{document}
\begin{multline}
\left[
1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{m \, t}{\sigma \, \sqrt{n}} - \frac{m^2 \, t^2}{\sigma^2 \, n} + \frac{1}{2} \frac{m^3 \, t^3}{\sigma^3 \, n^{3/2}} +
\right.
\\
\left.
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} -
\frac{\mathbb{E} [X_1^2]}{2} \frac{m \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{4} \frac{m^2 \, t^4}{\sigma^4 \, n^2} +
O \left( \frac{t^3}{n^{3/2}} \right)
\right]^n
\end{multline}
\end{document}
这用于\vphantom
强制括号大小相同。保存框只是为了避免输入两次代码。
\documentclass{article}
\usepackage{amsmath, amssymb}
\newsavebox{\leftbox}
\newsavebox{\rightbox}
\begin{document}
\savebox{\leftbox}{$\displaystyle
1 - \frac{m \, t}{\sigma \, \sqrt{n}} + \frac{1}{2} \frac{m^2 \, t^2}{\sigma^2 \, n} +
\frac{m \, t}{\sigma \, \sqrt{n}} - \frac{m^2 \, t^2}{\sigma^2 \, n} + \frac{1}{2} \frac{m^3 \, t^3}{\sigma^3 \, n^{3/2}} +$}
\savebox{\rightbox}{$\displaystyle
\frac{\mathbb{E} [X_1^2]}{2} \frac{t^2}{\sigma^2 \, n} -
\frac{\mathbb{E} [X_1^2]}{2} \frac{m \, t^3}{\sigma^3 \, n^{3/2}} +
\frac{\mathbb{E} [X_1^2]}{4} \frac{m^2 \, t^4}{\sigma^4 \, n^2} +
O \left( \frac{t^3}{n^{3/2}} \right)$}
\begin{multline}
\left[ \usebox\leftbox \vphantom{\usebox\rightbox} \right.
\\
\left. \usebox\rightbox \vphantom{\usebox\leftbox} \right]^n
\end{multline}
\end{document}