\[T_{N}(\mathbf{\tfrac{1}{2}},\mathbf{z})=\sum(-1)^{M+N}{\left(\tfrac{1}{2}%
\right)_{M}}\frac{E_{1}^{m_{1}}(\mathbf{z})\cdots E_{n}^{m_{n}}(\mathbf{z})}{m%
_{1}!\cdots m_{n}!},\]