Table of Integrals, Series, and Products (8th edition)(I.S.Gradshteyn,I.M.Ryzhik,Daniel Zwillinger, and Victor Moll) contains the following formula.(Page 693)
6.578 $\,$6.11
$$\int_{0}^{\infty} x^{\mu+1}K_{\mu}(ax)J_{\nu}(bx)J_{\nu}(cx)dx=\frac{1}{(2\pi)^{1/2}}a^{\mu}b^{-\mu-1}c^{-\mu-1}e^{-(\mu+\frac{1}{2})\pi i}(u^2-1)^{-\frac{1}{2}\mu-\frac{1}{4}} Q_{\nu-\frac{1}{2}}^{\mu+\frac{1}{2}}(u)$$
$$2bcu=a^2+b^2+c^2, \quad \mathrm{Re}\,a > |\mathrm{Im}\, b|+|\mathrm{Im}\,c|, \quad \mathrm{Re}\, \nu > -1, \quad \mathrm{Re}(\mu+\nu) > -1$$
As far as I've checked, this formula is wrong.
Does anyone know the correct formula?