\[T_{N}(\mathbf{b},\mathbf{z})=\sum\frac{{\left(b_{1}\right)_{m_{1}}}\cdots{%
\left(b_{n}\right)_{m_{n}}}}{m_{1}!\cdots m_{n}!}z_{1}^{m_{1}}\cdots z_{n}^{m_%
{n}},\]