拉盖尔多项式表的误差

Question

总共有 4 行，每行都写了一个方程环境。但是我的代码有问题。如果可以的话，请帮帮我。

    \begin{table}[H]
    \centering
    \caption{Laguerre polynomials}
    \begin{tabular}{l}
    \hline \\[0.5ex]
    \begin{equation}
    n=0
    \begin{cases}
    L_{0}^{1}(z)= \\
    L_{0}^{2}(z)= \\
    L_{0}^{3}(z)= \\
    L_{0}^{4}(z)= \\
    L_{0}^{5}(z)= \\
    \vdots
    \end{cases}
    \end{equation}
    \hline \\[0.5ex]
    \begin{equation}
    n=1
    \begin{cases}
    L_{1}^{1}(z)= \\
    L_{1}^{2}(z)= \\
    L_{1}^{3}(z)= \\
    L_{1}^{4}(z)= \\
    L_{1}^{5}(z)= \\
    \vdots 
    \end{cases}
    \end{equation}
    \hline \\[0.5ex]
    \begin{equation}
    n=2
    \begin{cases}
    L_{2}^{1}(z)= \\
    L_{2}^{2}(z)= \\
    L_{2}^{3}(z)= \\
    L_{2}^{4}(z)= \\
    L_{2}^{5}(z)= \\
    \vdots 
    \end{cases}
    \end{equation}
    \hline \\[0.5ex]
    \begin{equation}
    n=3
    \begin{cases}
    L_{3}^{1}(z)= \\
    L_{3}^{2}(z)= \\
    L_{3}^{3}(z)= \\
    L_{3}^{4}(z)= \\
    L_{3}^{5}(z)= \\
    \vdots
    \end{cases}
    \end{equation}
    \hline \\[0.5ex]
    $\vdots$
    \end{tabular}
    \end{table}

Answer 1

这是一个可行的代码，但如果您告诉我们您想要实现什么，它可以得到改进。

\documentclass{article}
\usepackage{amsmath}
\begin{document}
    \begin{table}
    \centering
    \caption{Laguerre polynomials}
    \begin{tabular}{l}
    \hline 
    $\displaystyle
    n=0
    \begin{cases}
    L_{0}^{1}(z)= \\
    L_{0}^{2}(z)= \\
    L_{0}^{3}(z)= \\
    L_{0}^{4}(z)= \\
    L_{0}^{5}(z)= \\
    \vdots
    \end{cases}
    $\\[0.5ex]
    \hline 
    $\displaystyle
    n=1
    \begin{cases}
    L_{1}^{1}(z)= \\
    L_{1}^{2}(z)= \\
    L_{1}^{3}(z)= \\
    L_{1}^{4}(z)= \\
    L_{1}^{5}(z)= \\
    \vdots 
    \end{cases}
    $\\[0.5ex]
    \hline 
    $\displaystyle
    n=2
    \begin{cases}
    L_{2}^{1}(z)= \\
    L_{2}^{2}(z)= \\
    L_{2}^{3}(z)= \\
    L_{2}^{4}(z)= \\
    L_{2}^{5}(z)= \\
    \vdots 
    \end{cases}
    $\\[0.5ex]
    \hline 
    $\displaystyle
    n=3
    \begin{cases}
    L_{3}^{1}(z)= \\
    L_{3}^{2}(z)= \\
    L_{3}^{3}(z)= \\
    L_{3}^{4}(z)= \\
    L_{3}^{5}(z)= \\
    \vdots
    \end{cases}
    $\\[0.5ex]
    \hline 
    $\vdots$
    \end{tabular}
    \end{table}
\end{document}