  The news function providing some relevant information about angular
distribution of gravitational radiation in axisymmetric black hole collisions
at the speed of light had been evaluated in the literature by perturbation
methods, after inverting second-order hyperbolic operators with variable
coefficients in two independent variables. More recent work has related the
appropriate Green function to the Riemann function for such a class of
hyperbolic operators in two variables. The present paper obtains an improvement
in the evaluation of the coefficients occurring in the second-order equation
obeyed by the Riemann function, which might prove useful for numerical
purposes. Eventually, we find under which conditions the original
Green-function calculation reduces to finding solutions of an inhomogeneous
second-order ordinary differential equation with a non-regular singular point.
