Opuscula Math. 35, no. 5 (2015), 803-823
http://dx.doi.org/10.7494/OpMath.2015.35.5.803

 
Opuscula Mathematica

Alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter

Mika Tanda

Abstract. We compute alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter and discuss the singularity structures of the Borel transforms of the WKB solution expressed in terms of its alien derivatives.

Keywords: hypergeometric differential equation, WKB solution, Voros coefficient, alien derivative, Stokes curve, fixed singularity.

Mathematics Subject Classification: 33C05, 34M40, 34M60.

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  • Mika Tanda
  • Interdisciplinary Graduate School of Science and Engineering, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan
  • Communicated by Yoshishige Haraoka.
  • Received: 2014-03-31.
  • Revised: 2015-02-03.
  • Accepted: 2015-02-05.
  • Published online: 2015-04-27.
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Cite this article as:
Mika Tanda, Alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter, Opuscula Math. 35, no. 5 (2015), 803-823, http://dx.doi.org/10.7494/OpMath.2015.35.5.803

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