  A scalar product for quasinormal mode solutions to Teukolsky's homogeneous
radial equation is presented. Evaluation of this scalar product can be
performed either by direct integration, or by evaluation of a confluent
hypergeometric functions. For direct integration, it is explicitly shown that
the quasinormal modes' radial functions are regular on a family of physically
bounded complex paths. The related scalar product will be useful for better
understanding analytic solutions to Teukolsky's radial equation, particularly
the quasi-normal modes, their potential spatial completeness, and whether the
quasi-normal mode overtone excitations may be estimated by spectral
decomposition rather than fitting. With that motivation, the scalar product is
applied to confluent Heun polynomials where it is used to derive their peculiar
orthogonality and eigenvalue properties. A potentially new relationship is
derived between the confluent Heun polynomials' scalar products and
eigenvalues. Using these results, it is shown for the first time that
Teukolsky's radial equation (and perhaps similar confluent Heun equations) are,
in principle, exactly tridiagonalizable. To this end, "canonical" confluent
Heun polynomials are conjectured.
