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), pp. 67-78. 
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     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 = {Loday-Richaud Mich\`ele},
     series = {Ast\'erisque},
     pages = {67--78},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {297},
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Joshi, Nalini; Kajiwara, Kenji; Mazzocco, Marta. Generating function associated with the determinant formula for the solutions of the Painlevé II equation, dans Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque, no. 297 (2004), pp. 67-78. http://archive.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

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

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

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

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

[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 | Zbl

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

[8] M. Jimbo, Unpublished work.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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[15] K. Okamoto - Private communication.

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

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

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

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

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