Lommel integral (involving Bessel functions)

Does anyone know how to evaluate the following integral (it's called a Lommel integral)

$\int (AJ_1(m\rho)+BY_1(-m\rho))^2\rho d\rho$

where $A$, $B$, $m$ are aribtrary complex constants and $\rho$ is real. $J_1$ is a Bessel function of the first kind (order one) and $Y_1$ is a Bessel function of the second kind (order one).

Thanks!!