Generating function associated with the determinant formula for the solutions of the Painlevé II equation
Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque no. 297  (2004), p. 67-78
@incollection{AST_2004__297__67_0,
     author = {Joshi, Nalini and Kajiwara, Kenji and Mazzocco, Marta},
     title = {Generating function associated with the determinant formula for the solutions of the Painlev\'e II equation},
     booktitle = {Analyse complexe, syst\`emes dynamiques, sommabilit\'e des s\'eries divergentes et th\'eories galoisiennes (II)},
     editor = {Loray-Richaud Mich\`ele},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {297},
     year = {2004},
     pages = {67-78},
     zbl = {1081.34087},
     mrnumber = {2135675},
     language = {en},
     url = {http://www.numdam.org/item/AST_2004__297__67_0}
}
Joshi, Nalini; Kajiwara, Kenji; Mazzocco, Marta. Generating function associated with the determinant formula for the solutions of the Painlevé II equation, in Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque, no. 297 (2004), pp. 67-78. http://www.numdam.org/item/AST_2004__297__67_0/

[1] M.J. Ablowitz & H. Segur - "Exact linearization of a Painlevé transcendent", Phys. Rev. Lett. 38 (1977), p. 1103-1106. | MR 442981

[2] H. Airault - "Rational solutions of Painlevé equations", Stud. Appl. Math. 61 (1979), p. 31-53. | MR 535866 | Zbl 0496.58012

[3] N. P. Erugin - "On the second transcendent of Painlevé", Dokl. Akad. Nauk BSSR 2 (1958), p. 139-142. | MR 132245

[4] H. Flaschka & A. C. Newell - "Monodromy and Spectrum Preserving Deformations I", Comm. Math. Phys. 76 (1980), p. 65-116. | MR 588248 | Zbl 0439.34005

[5] P. F. Hsieh & Y. Sibuya - Basic theory of ordinary differential equations, Universitext, Springer, New York, 1999. | MR 1697415 | Zbl 0924.34001

[6] K. Iwasaki, K. Kajiwara & T. Nakamura - "Generating function associated with the rational solutions of the Painlevé II equation", J. Phys. A: Math. Gen. 35 (2002), p. L207-L211. | MR 1913222 | Zbl 1040.33016

[7] M. Jimbo - "Monodromy problem and the boundary condition for some Painlevé equations", Publ. RIMS, Kyoto Univ. 18 (1982), p. 1137-1161. | MR 688949 | Zbl 0535.34042

[8] M. Jimbo, Unpublished work.

[9] A. I. Jimbo & T. Miwa - "Monodoromy preserving deformation of linear ordinary differential equations with rational coefficients. II", Physica: 2D (1981), p. 407-448. | MR 625446 | Zbl 1194.34166

[10] K. Kajiwara & T. Masuda - "A generalization of the determinant formulae for the solutions of the Painlevé II equation", J. Phys. A: Math. Gen. 32 (1999), p. 3763-3778. | MR 1694666 | Zbl 0943.34084

[11] K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta & Y. Yamada - "Determinant formulas for the Toda and discrete Toda equations", Funkcial. Ekvac. 44 (2001), p. 291-307. | MR 1865393 | Zbl 1145.37327

[12] K. Kajiwara & Y. Ohta - "Determinant structure of the rational solutions for the Painlevé II equation", J. Math. Phys. 37 (1996), p. 4693-4704. | MR 1408115 | Zbl 0865.34010

[13] Y. Murata - "Rational solutions of the second and the fourth Painlevé equations", Funkcial. Ekvac. 28 (1985), p. 1-32. | MR 803400 | Zbl 0597.34004

[14] M. Noumi & K. Okamoto - "Irreducibility of the second and the fourth Painlevé equations", Funkcial. Ekvac. 40 (1997), p. 139-163. | MR 1454468 | Zbl 0881.34052

[15] K. Okamoto - Private communication.

[16] J.-P. Ramis - Séries divergentes et théories asymptotiques, Panoramas & Synthèses, Société Mathématique de France, 1993. | MR 1272100 | Zbl 0830.34045

[17] H. Umemura & H. Watanabe - "Solutions of the second and fourth Painlevé equations I", Nagoya Math. J. 148 (1997), p. 151-198. | MR 1492945 | Zbl 0934.33029

[18] A.P. Vorob'Ev - "On the rational solutions of the second Painlevé equation", Differencial'nye Uravnenija 1 (1965), p. 79-81. | MR 188519 | Zbl 0221.34001

[19] W. Wasow - Asymptotic expansions for ordinary differential equations, Reprint of the 1965 edition, Robert E. Krieger Publishing Co., Huntington, N.Y., 1976. | MR 460820

[20] A. I. Yablonskii - Vesti Akad. Navuk. BSSR Ser. Fiz. Tkh. Nauk. 3 (1959), p. 30-35.