Opuscula Math. 35, no. 5 (2015), 775-802

Opuscula Mathematica

On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

Yoshitsugu Takei

Abstract. Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

Keywords: exact WKB analysis, WKB solution, multisummability.

Mathematics Subject Classification: 34M60, 34E20, 34M30, 40G10.

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  • Yoshitsugu Takei
  • RIMS, Kyoto University, Kyoto 606-8502, Japan
  • Communicated by P.A. Cojuhari.
  • Received: 2014-03-31.
  • Revised: 2014-08-08.
  • Accepted: 2014-12-15.
  • Published online: 2015-04-27.
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Cite this article as:
Yoshitsugu Takei, On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations, Opuscula Math. 35, no. 5 (2015), 775-802, http://dx.doi.org/10.7494/OpMath.2015.35.5.775

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