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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 $L=\frac{{d}^{2}}{d{z}^{2}}+\left(\frac{a}{z}-1\right)\frac{d}{dz}+\frac{b}{z}$, 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:
 34E05 Asymptotic expansions (ODE) 33C15 Confluent hypergeometric functions, Whittaker functions, ${}_{1}{F}_{1}$