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Zbl 0809.34007
Olde Daalhuis, A.B.; Olver, F.W.J.
Exponentially improved asymptotic solutions of ordinary differential equations. II: Irregular singularities of rank one. (English)
[J] Proc. R. Soc. Lond., Ser. A 445, No.1923, 39-56 (1994). ISSN 0080-4630

The authors consider the asymptotic expansions of solutions of the general homogeneous linear differential equations of the second order in the neighbourhood of an irregular singularity of rank one. The re- expansions for the optimal remainder terms in these asymptotic series are given. The re-expansions are obtained in the terms of generalized exponential integrals. The explicit asymptotic expansions for the higher coefficients of the original asymptotic solutions are also constructed.\par \{For part I see [the first author, SIAM J. Math. Anal. 24, 756-767 (1993; Zbl 0779.34048)]\}.
[S.Mazanik (Minsk)]

MSC 2000:: *34M35 Singularities, monodromy, local behavior of solutions, normal forms
34A25 Analytical theory of ODE
34E05 Asymptotic expansions (ODE)

Keywords: asymptotic expansions; homogeneous linear differential equations; irregular singularity of rank one

Citations: Zbl 0779.34048

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