If there are expansions of the form (37) – (38), we have seen that can be computed according to Equation (39). As a consequence, it is of interest to ask if the limit on the right-hand side of this equation always exists. Due to [79, Corollary 6.9, p. 1009], the answer is yes. As a consequence, we are naturally led to the following definition.

Definition 4 Let be a solution to Equations (16)–(17) and let . Then we define the asymptotic velocity at to be

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