\[S_{1}(\nu,z)=\sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k}}{\Gamma%
\left(k\!+\!\tfrac{1}{2}\nu+1\right)\Gamma\left(k\!-\!\tfrac{1}{2}\nu\!+\!1%
\right)},\]