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Zbl 1136.34322
Byatt-Smith, J. G.
The Borel transform and its use in the summation of asymptotic expansions. (English)
[J] Stud. Appl. Math. 105, No. 2, 83-113 (2000). ISSN 0022-2526; ISSN 1467-9590/e

Summary: The solution of connection problems on the real line (the $x$ axis) often give asymptotic expansions which are either even or odd. This gives rise to ``identically zero" expansions, that is, an asymptotic expansion in which all terms are identically zero at the origin. We show that the Borel transform of these problems have solutions that provide integral representations of the solution. The evaluation of these integrals, as $x\to 0$, allows us to compute the exponentially small term that these ``identically zero" expansions represent.

MSC 2000:: *34E10 Asymptotic perturbations (ODE)
34M30 Asymptotics, summation methods
34M40 Stokes phenomena and connection problems

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