\[\mathbf{E}_{n}\left(z\right)=-\mathbf{H}_{n}\left(z\right)+\frac{1}{\pi}\sum_{%
k=0}^{m_{1}}\frac{\Gamma\left(k+\tfrac{1}{2}\right)}{\Gamma\left(n\!+\!\tfrac{%
1}{2}\!-\!k\right)}(\tfrac{1}{2}z)^{n-2k-1},\]