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

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

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

Thanks!!