\[B_{s}(\xi)=-A_{s}^{\prime}(\xi)+\frac{1}{\xi^{1/2}}\int_{0}^{\xi}\left(\psi(v)%
A_{s}(v)-\left(\nu+\tfrac{1}{2}\right)A_{s}^{\prime}(v)\right)\frac{\,\mathrm{%
d}v}{v^{1/2}},\]