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!!