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