${\int }_0^{\infty }\frac{t^{\nu +1}{J}_{\nu }\left(at\right)}{{(t^2+b^2)}^{\mu +1}}\mathrm{mathrm}dt=\frac{a^{\mu }{b}^{\nu -\mu }}{2^{\mu }\Gamma (\mu +1)}{K}_{\nu -\mu }\left(ab\right)$