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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 $L={d\sp 2\over dz\sp 2}+\bigl({a\over z}-1\bigr){d\over dz}+{b\over z}$, 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)

34E05Asymptotic expansions (ODE)
33C15Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$
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