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.

Full text (pdf)

• Mika Tanda
• Interdisciplinary Graduate School of Science and Engineering, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan
• Revised: 2015-02-03.
• Accepted: 2015-02-05.