\[S_{{\mu},{\nu}}\left(z\right)=s_{{\mu},{\nu}}\left(z\right)+2^{\mu-1}\Gamma%
\left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}\right)\Gamma\left(\tfrac{1}%
{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}\right)\*\left(\sin\left(\tfrac{1}{2}(\mu-%
\nu)\pi\right)\,J_{\nu}\left(z\right)-\cos\left(\tfrac{1}{2}(\mu-\nu)\pi\right%
)\,Y_{\nu}\left(z\right)\right),\]