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:<math>\mathfrak{P}\{\mathcal{B}\} = \prod_{\beta \in \mathcal{B}}(\mathcal{E} + \{\beta\})</math>
which leads to the relation
:<math>\begin{matrixalign}A(z) &{} = & \prod_{\beta \in \mathcal{B}}(1 + z^{|\beta|}) \\
&{} = & \prod_{n=1}^{\infty}(1 + z^{n})^{B_{n}} \\
&{} = & \exp \left ( \ln \prod_{n=1}^{\infty}(1 + z^{n})^{B_{n}} \right ) \\
&{} = & \exp \left ( \sum_{n = 1}^{\infty} B_{n} \ln(1 + z^{n}) \right ) \\
&{} = & \exp \left ( \sum_{n = 1}^{\infty} B_{n} \cdot \sum_{k = 1}^{\infty} \frac{(-1)^{k-1}z^{nk}}{k} \right ) \\
&{} = & \exp \left ( \sum_{k = 1}^{\infty} \frac{(-1)^{k-1}}{k} \cdot \sum_{n = 1}^{\infty}B_{n}z^{nk} \right ) \\
&{} = & \exp \left ( \sum_{k = 1}^{\infty} \frac{(-1)^{k-1} B(z^{k})}{k} \right )
\end{matrixalign}</math>
where the expansion
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