Does anyone have suggestions for how to approach this integral that I came across in a project? Can one apply identities to make it doable analytically or using Mathematica? I tried but couldn't get very far. Thanks a lot!
$$\int_0^{\infty}dx\ x^2 e^{-\epsilon x}J_{n-1}(ix)J_{n+1}(ix)\frac{Y_n(ix)}{J_n(ix)}.$$
Here $J_n$ and $Y_n$ are Bessel functions of the first and second kind respectively.