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The Borel transform and its use in the summation of asymptotic expansions. (English) Zbl 1136.34322
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 x0, allows us to compute the exponentially small term that these “identically zero” expansions represent.
MSC:
34E10Perturbations, asymptotics (ODE)
34M30Asymptotics, summation methods (ODE in the complex domain)
34M40Stokes phenomena and connection problems (ODE in the complex domain)