Multiple-scale analysis for Painlevé transcendents with a large parameter

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Department of Mathematics and Physics, Kinki University, Higashi-Osaka, 577 Japan

[AKT1] T. Aoki, T. Kawai and Y. Takei, The Bender-Wu analysis and the Voros theory, in: ICM-90 Satellite Conf. Proc. ``Special Functions'' (M. Kashiwara and T. Miwa, editors), Springer-Verlag, 1991, 1-29.
[AKT2] T. Aoki, T. Kawai and Y. Takei, Algebraic analysis of singular perturbations - On exact WKB analysis, Sugaku Expositions 8 (1995), 217-240.
[AKT3] T. Aoki, T. Kawai and Y. Takei, WKB analysis of Painlevé transcendents with a large parameter, II, in preparation.
[BO] C. M. Bender and S. T. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978.
[JK] N. Joshi and M. Kruskal, Connection results for the first Painlevé equation, in: Painlevé transcendents (D. Levi and P. Winternitz, editors), Plenum Press, New York, 1992, 61-79.
[KT] T. Kawai and Y. Takei, WKB analysis of Painlevé transcendents with a large parameter, I, Adv. Math. 118 (1996), 1-33.
[V] A. Voros, The return of the quartic oscillator. The complex WKB method, Ann. Inst. H. Poincaré Sect. A (N.S.) 39 (1983), 211-338.