∫ 0 ∞ t ν + 1 J ν ( a t ) ( t 2 + b 2 ) μ + 1 d t = a μ b ν − μ 2 μ Γ ( μ + 1 ) K ν − μ ( a b ) \int_{0}^{\infty}\frac{t^{\nu+1}J_{\nu}\left(at\right)}{(t^{2}+b^{2})^{\mu+1}}\mathrm{d}t=\frac{a^{\mu}b^{\nu-\mu}}{2^{\mu}\Gamma\left(\mu+1\right)}K_{\nu-\mu}\left(ab\right)