  As shown by Teukolsky, the master equation governing the propagation of weak
radiation in a black hole spacetime can be separated into four ordinary
differential equations, one for each spacetime coordinate. (``Weak'' means the
radiation's amplitude is small enough that its own gravitation may be
neglected.) Unfortunately, it is difficult to accurately compute solutions to
the separated radial equation (the Teukolsky equation), particularly in a
numerical implementation. The fundamental reason for this is that the Teukolsky
equation's potentials are long ranged. For non-spinning black holes, one can
get around this difficulty by applying transformations which relate the
Teukolsky solution to solutions of the Regge-Wheeler equation, which has a
short-ranged potential. A particularly attractive generalization of this
approach to spinning black holes for gravitational radiation (spin weight s =
-2) was given by Sasaki and Nakamura. In this paper, I generalize Sasaki and
Nakamura's results to encompass radiation fields of arbitrary integer spin
weight, and give results directly applicable to scalar (s = 0) and
electromagnetic (s = -1) radiation. These results may be of interest for
studies of astrophysical radiation processes near black holes, and of programs
to compute radiation reaction forces in curved spacetime.
