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\documentclass[DIV=30]{scrartcl}
\usepackage{amsmath}
\begin{document}
\begin{multline*}
\left(\begin{matrix}
f^{i_1}(1(i_1))&&f^{i_2}(1(i_2))&\cdots&f^{i_{k-1}}(1(i_{k-1}))&&f^{i_k}(1(i_{k}))&&\xi_n\\\\\\
&f^{i'_1}(1(i'_1))&&\cdots&&f^{i'_{k-1}}(1(i'_{k-1}))&&f^0(1(0))&&g^0(1(0))
\end{matrix}\right.\\
\left.\begin{matrix}
&g^{i_1}(1(i_1))&&g^{i_2}(1(i_2))&\cdots &g^{i_{k-1}}(1(i_{k-1}))&&g^{i_k}(1(i_{k}))\\\\\\
&&g^{i'_1}(1(i'_1))&& \cdots g^{i'_{k-2}}(1(i'_{k-2}))&&g^{i'_{k-1}}(1(i'_{k-1}))
\end{matrix}\right)
\end{multline*}
\end{document}
 
 
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