\[\int_{0}^{\infty}e^{ibt}Y_{0}\left(at\right)\,\mathrm{d}t=\begin{cases}(2i/\pi%
)(a^{2}-b^{2})^{-\frac{1}{2}}\operatorname{arcsin}\left(b/a\right),&0\leq b<a,%
\\
(b^{2}-a^{2})^{-\frac{1}{2}}\left(-1+\dfrac{2i}{\pi}\ln\left(\dfrac{a}{b+(b^{2%
}-a^{2})^{\frac{1}{2}}}\right)\right),&0<a<b.\end{cases}\]