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Zbl 1185.33005
López, José L.; Pagola, Pedro J.
The confluent hypergeometric functions $M(a,b;z)$ and $U(a,b;z)$ for large $b$ and $z$. (English)
[J] J. Comput. Appl. Math. 233, No. 6, 1570-1576 (2010). ISSN 0377-0427

Using a variant of Laplace's method for integrals, the authors obtain new and complete asymptotic expansions for the confluent hypergeometric functions $M(a,b;z)$ and $U(a,b;z)$ for large $b$ and $z$. For both functions the starting point is the classical integral representation and the asymptotic expansions -- which are not of Poincaré type - are different in three classes: for $b<z+a+1$, for $b>z+a+1$, and for $b=z+a+1$.
[Roelof Koekoek (Delft)]

MSC 2000:: *33C15 Confluent hypergeometric functions
41A60 Asymptotic problems in approximation

Keywords: asymptotic expansions; confluent hypergeometric functions

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