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Exponentially-improved asymptotic solutions of ordinary differential equations. I: The confluent hypergeometric function. (English) Zbl 0779.34048
To establish exponentially-improved asymptotics for the confluent hypergeometric function U (and thus to improve an earlier result following from the integral representation of U), the author develops a new form of asymptotic analysis for the linear differential operator L=d 2 dz 2 +a z - 1d dz+b z, with constant a and b. This approach is based on constructing a finite series of special functions which, when operated upon by L, provide the desired terms except for an asymptotically small error.
Reviewer: J.Šimša (Brno)

MSC:
34E05Asymptotic expansions (ODE)
33C15Confluent hypergeometric functions, Whittaker functions, 1 F 1