\[\int_{0}^{\infty}t^{\mu-1}e^{-at}Y_{\nu}\left(bt\right)\,\mathrm{d}t=\cot\left%
(\nu\pi\right)\frac{(\tfrac{1}{2}b)^{\nu}\Gamma\left(\mu+\nu\right)}{(a^{2}+b^%
{2})^{\frac{1}{2}(\mu+\nu)}}\*\mathbf{F}\left(\frac{\mu+\nu}{2},\frac{1-\mu+%
\nu}{2};\nu+1;\frac{b^{2}}{a^{2}+b^{2}}\right)-\csc\left(\nu\pi\right)\frac{(%
\tfrac{1}{2}b)^{-\nu}\Gamma\left(\mu-\nu\right)}{(a^{2}+b^{2})^{\frac{1}{2}(%
\mu-\nu)}}\*\mathbf{F}\left(\frac{\mu-\nu}{2},\frac{1-\mu-\nu}{2};1-\nu;\frac{%
b^{2}}{a^{2}+b^{2}}\right),\]