\[B_{s}(\xi)=\begin{cases}\dfrac{1}{2\xi^{1/2}}\displaystyle\int_{0}^{\xi}\left(%
\psi(v)A_{s}(v)-A_{s}^{\prime\prime}(v)\right)\dfrac{\,\mathrm{d}v}{v^{1/2}},&%
\xi>0,\\
\dfrac{1}{2(-\xi)^{1/2}}\displaystyle\int_{\xi}^{0}\left(\psi(v)A_{s}(v)-A_{s}%
^{\prime\prime}(v)\right)\dfrac{\,\mathrm{d}v}{(-v)^{1/2}},&\xi<0,\end{cases}\]