ANALYTIC SOLUTIONS OF THE REGGE-WHEELER EQUATION AND THE POST-MINKOWSKIAN EXPANSION

Analytic solutions of the Regge-Wheeler equation are presented in the form of a series of hypergeometric functions and Coulomb wave function s which have different regions of convergence. Relations among these s olutions are established. The series solutions are given as the Post-M inkowskian expansion with respect to the parameter epsilon=2M omega, M being the mass of a black hole. This expansion corresponds to the pos t-Newtonian expansion when they are applied to the gravitational radia tion from a particle in a circular orbit around a black hole. These so lutions can also be useful for numerical computations.