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Zbl 0779.34048
Olver, F.W.J.
Exponentially-improved asymptotic solutions of ordinary differential equations. I: The confluent hypergeometric function. (English)
[J] SIAM J. Math. Anal. 24, No.3, 756-767 (1993). ISSN 0036-1410; ISSN 1095-7154/e

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.
[J.Šimša (Brno)]

MSC 2000:: *34E05 Asymptotic expansions (ODE)
33C15 Confluent hypergeometric functions

Keywords: factorial series; gamma function; superasymptotics; exponentially- improved asymptotics; confluent hypergeometric function; asymptotic analysis; linear differential operator; finite series of special functions

Cited in: Zbl 0809.34007

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