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我该如何对齐 (1) 和 (2)？

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我该如何对齐 (1) 和 (2)？

下面的代码

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage{amsthm}
\usepackage{amsmath}
\usepackage[left=1.5in, right=1.5in, top=0.5in]{geometry}


\newtheorem{definition}{Definition}
\newtheorem{theorem}{Theorem} 
\theoremstyle{remark}


\begin{document}
\title{Extra Credit}
\maketitle

\begin{definition}
If f is analytic at $z_0$, then the series

$$f(z_0) + f'(z_0)(z-z_0) + \frac{f''(z_0)}{2!}(z-z_0)^2 + \cdots = \sum_{n=0}^{\infty} \frac{f^{(n)}(z_0)}{n!}(z-z_0)^n \hspace{1cm}(1)$$ 

is called the Taylor series for f around $z_0$.
\end{definition}

\begin{theorem}
If f is analytic inside and on the simple closed positively oriented contour $\Gamma$ and if $z_0$ is any point inside $\Gamma$, then
$$f^{(n)}(z_0) = \frac{n!}{2\pi i} \int_{\Gamma} \frac{f(\zeta)}{(\zeta - z_0)^{n+1}}d\zeta \hspace{1cm} (n=1,2,3, \cdots )$$ \hfill (2)
\end{theorem}\hrulefill

生产在此处输入图片描述

我怎样才能对齐 (1) 和 (2)，并且让 (2) 与 (n=1,2,3,...) 位于同一条线上？

答案1

我强烈建议使用不同的方法：

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage{amsthm}
\usepackage{amsmath}
\usepackage[left=1.5in, right=1.5in, top=0.5in]{geometry}% I do not recommend to use this naiv canons of page construction for typographic reasons.  
\usepackage[noabbrev]{cleveref}%new package

\newtheorem{definition}{Definition}
\newtheorem{theorem}{Theorem} 
\theoremstyle{remark}

\begin{document}
\title{Extra Credit}
\maketitle

\begin{definition}
If f is analytic at $z_0$, then the series
\begin{align}%observe that empty line is removed
    f(z_0) + f'(z_0)(z-z_0) + \frac{f''(z_0)}{2!}(z-z_0)^2 + \cdots = \sum_{n=0}^{\infty} \frac{f^{(n)}(z_0)}{n!}(z-z_0)^n \label{eq:Taylor} 
\end{align}%observe that empty line is removed
is called the \emph{Taylor series} for f around $z_0$.%The definition is not in italics here to emphasize the term. 
\end{definition}

\begin{theorem}
If f is analytic inside and on the simple closed positively oriented contour $\Gamma$ and if $z_0$ is any point inside $\Gamma$, then
\begin{align}
    f^{(n)}(z_0) = \frac{n!}{2\pi i} \int_{\Gamma} \frac{f(\zeta)}{(\zeta - z_0)^{n+1}}d\zeta \hspace{1cm} (n=1,2,3, \cdots ).%every parenthesis should be ended with a dot. 
\end{align}
\end{theorem}

\noindent\hrulefill %alternative:  \hrule

You can use refer to the equation by: \eqref{eq:Taylor} or \cref{eq:Taylor}. %This is the usual approach to refer to formulas. 

\end{document}

在此处输入图片描述

请阅读代码中的注释并 $$、\[、align、equation 和 displaymath 之间有什么区别？. 其他有用的人员写在https://ctan.org/pkg/short-math-guide，https://ctan.org/pkg/lshort-english， 和对于 LaTeX 初学者来说有哪些好的学习资源？。

答案2

使用另一种方法，equation环境如下：

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage{amsthm}
\usepackage{amsmath}
\usepackage[left=1.5in, right=1.5in, top=0.5in]{geometry}


\newtheorem{definition}{Definition}
\newtheorem{theorem}{Theorem} 
\theoremstyle{remark}

\begin{document}
    \title{Extra Credit}
    \maketitle

    \begin{definition}
        If f is analytic at $z_0$, then the series

        \begin{equation}
            f(z_0) + f'(z_0)(z-z_0) + \frac{f''(z_0)}{2!}(z-z_0)^2 + \cdots = \sum_{n=0}^{\infty} \frac{f^{(n)}(z_0)}{n!}(z-z_0)^n
        \end{equation}

        is called the Taylor series for f around $z_0$.
    \end{definition}

    \begin{theorem}
        If f is analytic inside and on the simple closed positively oriented contour $\Gamma$ and if $z_0$ is any point inside $\Gamma$, then
        \begin{equation}
            f^{(n)}(z_0) = \frac{n!}{2\pi i} \int_{\Gamma} \frac{f(\zeta)}{(\zeta - z_0)^{n+1}}d\zeta \hspace{1cm} (n=1,2,3, \cdots )
        \end{equation}
    \end{theorem}
    \hrulefill
\end{document}

答案3

(La)TeX 的一个主要功能是它能够自动为您编号章节、定理、列表项等。这包括方程式！使用

\begin{equation}
\label{somename}
    e=mc^2
\end{equation}

创建一个按顺序带有下一个数字的方程式，您可以使用 引用它\eqref{somename}。就像其他自动编号的东西一样，您可以在这个方程式之前插入一个新的编号方程式，所有数字都会正确更新。您可以使用 环境创建未编号的方程式equation*（或者，输入更少的文字\[ ... \]）。其他类似方程式的环境也有一个*不编号的版本。

请注意不建议用于$$...$$LaTeX 中的方程式。

（此外，我强烈建议对同一系列中的所有定义、定理等进行编号。当看到引理 3 和定义 5 无法提示您是否应该向前看还是向后看时，在长文档中寻找定理 4 真的很烦人。）

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