Proc. Japan Acad. Ser. A Math. Sci. 83 (5), 63-68, (May 2007) DOI: 10.3792/pjaa.83.63
Hideaki Wakako, Yoshitsugu Takei
KEYWORDS: Exact WKB analysis, connection formula, third Painlevé equation, 34M55, 34M60, 34M40
Exact WKB analysis for instanton-type solutions of the degenerate third Painlevé equation of type $(D_8)$ is discussed. Explicit connection formulas are obtained through computations of the monodromy data of the underlying linear equations.