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Alien derivatives of the WKB solutions of the gauss hypergeometric differential equation with a large parameter

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We compute alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter and discuss the singularity structures of the Borel transforms of the WKB solution expressed in terms of its alien derivatives.
Rocznik
Strony
803--823
Opis fizyczny
Bibliogr. 19 poz., rys.
Twórcy
autor
  • Interdisciplinary Graduate School of Science and Engineering Kinki University Higashi-Osaka Osaka 577-8502, Japan
Bibliografia
  • [1] T. Aoki, K. Iwaki, T. Takahashi, Exact WKB analysis of Schrodinger equations with a Stokes curve of loop type, in preparation.
  • [2] T. Aoki, T. Kawai, Y. Takei, The Bender-Wu Analysis and the Voros Theory, [in:] Special Functions, Springer, 1991, 1-29.
  • [3] T. Aoki, T. Iizuka, Classification of Stokes graphs of second order Fuchsian differential equations of genus two, Publ. RIMS, Kyoto Univ. 43 (2007), 241-276.
  • [4] T. Aoki, M. Tanda, Characterization of Stokes graphs and Voros coefficients of hyperge-ometric differential equations with a large parameter, RIMS Kokyuroku Bessatsu B40 (2013), 147-162.
  • [5] T. Aoki, M. Tanda, Borel sums of Voros coefficients of hype.rgeome.tric differential equa­tions with a large parameter, RIMS Kokyuroku., Kyoto Uni. 1861 (2013), 17-24.
  • [6] T. Aoki, M. Tanda, Parametric Stokes phenomena of the Gauss hypergeometric differ­ential equation with a large parameter, submitted.
  • [7] B. Candelpergher, M.A. Coppo, E. Delabaere, La sommation de Ramanujan, L'Enseignement Mathematique 43 (1997), 93-132.
  • [8] E. Delabaere, H. Dillinger, F. Pham, Resurgence de Voros et periodes des courbes hy-perelliptiques, Ann. Inst. Fourier, Grenoble, 43 (1993), 153-199.
  • [9] E. Delabaere, F. Pham, Resurgent methods in semi-classical asymptotics, Ann. Inst. Henri Poincare 71 (1999), 1-94.
  • [10] J. Ecalle, Les fonction resurgentes. Tome I., Publications Mathematiques d'Orsay 81, Universite de Paris-Sud, Department de Mathematique, Orsay (1981), 247 pp.
  • [11] K. Iwaki, T. Nakanishi, Exact WKB analysis and cluster algebras, J. Phys. A 47 (2014), 474009.
  • [12] T. Kawai, Y. Takei, Exact WKB analysis and cluster algebras Algebraic Analysis of Sin­gular Perturbation Theory, Translation of Mathematical Monographs, vol. 227, AMS, 2005.
  • [13] T. Koike, R. Schafke, On the Borel summability of WKB solutions of Schrodinger equations with polynomial potential and its application, to appear in RIMS Kokyuroku Bessatsu.
  • [14] T. Koike, Y. Takei, On the Voros coefficient for the Whittaker equation with a large parameter - Some progress around Sato's conjecture in exact WKB analysis, Publ. RIMS, Kyoto Univ. 47 (2011), 375-396.
  • [15] D. Sauzin, Resurgent functions and splitting problems, RIMS Kokyuroku 1493 (2006), 48-117.
  • [16] D. Sauzin, Introduction to 1-summability and resurgence, arXiv:1405.0356 (HAL--00860032), 2014.
  • [17] Y. Takei, Sato's conjecture for the Weber equation and transformation theory for Schrodinger equations with a merging pair of turning points, RIMS Kokyuroku Bessatsu BIO (2008), 205-224.
  • [18] M. Tanda, Exact WKB analysis of hypergeometric differential equations, to appear in RIMS Kokyuroku Bessatsu.
  • [19] M. Tanda, Parametric Stokes phenomena of the Gauss hypergeometric differential equa­tion with a large parameter, Doctoral Thesis, Kinki University, 2014.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f11c21ed-2e7c-41f0-bc4e-e0026c06d150
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