## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 68, Number 3 (2016), 1099-1132.

### Parametric Stokes phenomena of the Gauss hypergeometric differential equation with a large parameter

#### Abstract

Stokes phenomena with respect to parameters are investigated for the Gauss hypergeometric differential equation with a large parameter. For this purpose, the notion of the Voros coefficient is introduced for the equation. The explicit forms of the Voros coefficients are given as well as their Borel sums. By using them, formulas which describe the Stokes phenomena are obtained.

#### Article information

**Source**

J. Math. Soc. Japan Volume 68, Number 3 (2016), 1099-1132.

**Dates**

First available in Project Euclid: 19 July 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.jmsj/1468956161

**Digital Object Identifier**

doi:10.2969/jmsj/06831099

**Mathematical Reviews number (MathSciNet)**

MR3523540

**Zentralblatt MATH identifier**

06642406

**Subjects**

Primary: 33C05: Classical hypergeometric functions, $_2F_1$

Secondary: 34M40: Stokes phenomena and connection problems (linear and nonlinear) 34M60: Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]

**Keywords**

hypergeometric differential equation WKB solution Voros coefficient Borel sum Stokes phenomena

#### Citation

AOKI, Takashi; TANDA, Mika. Parametric Stokes phenomena of the Gauss hypergeometric differential equation with a large parameter. J. Math. Soc. Japan 68 (2016), no. 3, 1099--1132. doi:10.2969/jmsj/06831099. https://projecteuclid.org/euclid.jmsj/1468956161.