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\fbox{ %
\parbox{10cm}{%
\begin{equation}
f(x) = \sum \limits_{n = - \infty}^{+ \infty}c_{n} (z - a)^{n} =
\left\{ \begin{array} {rrr}  c_{0} + c_{1}(z-a) + c_{2} (z-a)^{2} + \dots + c_{n} (z-a)^{n} + \cdots \\
c_{-1} (z-a)^{-1} + c_{-n}(z-a)^{-2} + \cdots \\
+ c_{-n}(z-a)^{-n}+ \cdots 
\end{array} \right .
\end{equation} }}

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\documentclass{scrartcl}
\usepackage{xcolor}
\usepackage{amsmath}
\begin{document}
\fcolorbox{red}{white}{ %
\parbox{10cm}{%
\begin{equation}
f(x) = \sum \limits_{n = - \infty}^{+ \infty}c_{n} (z - a)^{n} =
\begin{cases}c_{0} + c_{1}(z-a) + c_{2} (z-a)^{2} + \dots + c_{n} (z-a)^{n} + \cdots \\
c_{-1} (z-a)^{-1} + c_{-n}(z-a)^{-2} + \cdots \\
+ c_{-n}(z-a)^{-n}+ \cdots\end{cases}
\end{equation} }}
\end{document}