\[\int_{0}^{\infty}\frac{K_{\mu}\left(at\right)J_{\nu}\left(bt\right)}{t^{%
\lambda}}\,\mathrm{d}t=\frac{b^{\nu}\Gamma\left(\frac{1}{2}\nu-\frac{1}{2}%
\lambda+\frac{1}{2}\mu+\frac{1}{2}\right)\Gamma\left(\frac{1}{2}\nu-\frac{1}{2%
}\lambda-\frac{1}{2}\mu+\frac{1}{2}\right)}{2^{\lambda+1}a^{\nu-\lambda+1}}\*%
\mathbf{F}\left(\frac{\nu-\lambda+\mu+1}{2},\frac{\nu-\lambda-\mu+1}{2};\nu+1;%
-\frac{b^{2}}{a^{2}}\right),\]