\[\left.\frac{\partial Y_{\nu}\left(x\right)}{\partial\nu}\right|_{\nu=-\frac{1}%
{2}}=-\sqrt{\frac{2}{\pi x}}\left(\operatorname{Ci}\left(2x\right)\sin x-\left%
(\operatorname{Si}\left(2x\right)-\pi\right)\cos x\right).\]