Exponentially improved asymptotics for anharmonic eigenvalues

Alvarez, G., Howls, C.J. and Silverstone, H. (2000) Exponentially improved asymptotics for anharmonic eigenvalues. Howls, Christopher J., Kawai, Takahiro and Takei, Yoshitsugu (eds.) In Toward the exact WKB analysis of differential equations, linear or non-linear. Kyoto University Press. pp. 121-134 .

Abstract

Contents: Part I. Exact WKB analysis of linear differential equations: Takahiro Kawai and Yoshitsugu Takei, Introduction-Exact WKB analysis of linear differential equations; its background and prospect (3-7); Takashi Aoki, Takahiro Kawai and Yoshitsugu Takei, On a complete description of the Stokes geometry for higher order ordinary differential equations with a large parameter via integral representations (9, 11-14); Setsuro Fujiié and Thierry Ramond, Exact WKB analysis and the Langer modification with application to barrier top resonances (9, 15-31); Naofumi Honda, Microlocal Stokes phenomena for holonomic modules (9, 33-38); Tatsuya Koike, On a regular singular point in the exact WKB analysis (9-10, 39-53); Tatsuya Koike, Asymptotics of the spectrum of Heun's equation and the exact WKB analysis (10, 55-70); Frédéric Pham, Multiple turning points in exact WKB analysis (variations on a theme of Stokes) (10, 71-85); Kôichi Uchiyama, Graphical illustration of Stokes phenomenon of integrals with saddles (10, 87-95); André Voros, Exact quantization method for the polynomial 1D Schrödinger equation (10, 97-108);
Part II. Hyperasymptotics and asymptotics beyond all orders: C. J. Howls, Introduction-development of exponential and hyper-asymptotics (111-118); Gabriel Álvarez, Christopher J. Howls and Harris J. Silverstone, Connection formula, hyperasymptotics, and Schrödinger eigenvalues: dispersive hyperasymptotics and the anharmonic oscillator (119, 121-134); Ovidiu Costin and Rodica D. Costin, Asymptotic structure of movable singularities of solutions of nonlinear analytic differential systems (119, 135-143); E. Delabaere and C. J. Howls, Hyperasymptotics for multidimensional Laplace integrals with boundaries (119, 145-163); J. R. King [John Robert King], Interacting Stokes lines (119, 165-178); Hideyuki Majima, A vanishing theorem in asymptotic analysis with asymptotic estimates of coefficients of "asymptotic series" in several variables (120, 179-187); A. B. Olde Daalhuis, On the Borel transform of the uniform asymptotic expansion of Bessel functions of large order (120, 189-195);
Part III. Asymptotic analysis and structure of non-linear differential equations: Takahiro Kawai and Yoshitsugu Takei, Introduction (199-202); Takashi Aoki, Takahiro Kawai and Yoshitsugu Takei, Can we find a new deformation of SL_J with respect to the parameters contained in ( P_J) (203, 205-208); A. R. Its and A. A. Kapaev, The irreducibility of the second Painlevé equation and the isomonodromy method (203, 209-222); Nalini Joshi, True solutions asymptotic to formal WKB solutions of the second Painlevé equation with large parameter (203, 223-229); Takahiro Kawai, Natural boundaries revisited through differential equations, infinite order or non-linear (203-204, 231-243); Masatoshi Noumi and Yasuhiko Yamada, Affine Weyl group symmetries in Painlevé type equations (204, 245-259); Kyoichi Takano, Defining manifolds for Painlevé equations (204, 261-269); Yoshitsugu Takei, An explicit description of the connection formula for the first Painlevé equation (204, 271-296).

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Contributors

Author: C.J. Howls

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