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