Analytic solutions of the Regge-Wheeler equation are presented in the form of a series of hypergeometric functions and Coulomb wave functions which have different regions of convergence. Relations among these solutions are established. The series solutions are given as the Post-Minkowskian expansion with respect to the parameter ϵ≡2Mω, M being the mass of a black hole. This expansion corresponds to the post-Newtonian expansion when they are applied to the gravitational radiation from a particle in a circular orbit around a black hole. These solutions can also be useful for numerical computations.
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Mano et al. (1996) studied this question.