<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\input{_preamble}
\begin{document}
    \myeqs{
        \boldsymbol{P}_i^{(k)}=
        \begin{cases}
            \boldsymbol{P}_{i}^{(0)} &amp; k=0 \\[2mm]
            \left.\begin{cases}
                      \boldsymbol{0} &amp; u_{i+p+1}^{{(0)}} = u_{i+k}^{{(0)}}\\[2mm]
                      \frac{p-k+1}{u_{i+p+1}^{{(0)}} - u_{i+k}^{{(0)}}} \left( \boldsymbol{P}_{i+1}^{(k-1)} - \boldsymbol{P}_{i}^{(k-1)} \right) &amp; \text{else}%u_{i+p+1} \neq u_{i+k}\\[2mm]
            \end{cases}\right|&amp; k&gt;0 \\
        \end{cases}
    }
\end{document}
</pre></body></html>