Journal of the Mathematical Society of Japan

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

Takashi AOKI and Mika TANDA

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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.


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References

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