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Book Review

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Book Information:

Authors: V. I. Gromak, I. Laine and S. Shimomura
Title: Painleve differential equations in the complex plane
Additional book information: de Gruyter Studies in Mathematics, volume 28, Walter de Gruyter, Berlin, 2002, viii + 303 pp., ISBN 3-11-017379-4, $89.95

References [Enhancements On Off] (What's this?)

  • [B] L. Bieberbach, Theorie der gewöhnlichen Differentialgleichungen, Springer, 1965. MR 31:408
  • [B1] P. Boutroux, Sur quelques propriétés des fonctions entières, Acta. Math. 28 (1904), 97-224.
  • [B2] P. Boutroux, Recherches sur les transcendentes de M. Painlevé et l'étude asymptotique des équations différentielles du seconde ordre, Ann. École Norm. Supér. 30 (1913), 255-375; and Ann. École Norm. Supér. 31 (1914), 99-159.
  • [HL1] A. Hinkkanen, I. Laine, Solutions of the first and second Painlevé equations are meromorphic, Journal d'Analyse Math. 79 (1999), 345-377. MR 2001d:34149
  • [HL2] A. Hinkkanen, I. Laine, Solutions of a modified third Painlevé equation are meromorphic, Journal d'Analyse Math. 85 (2001), 323-337. MR 2003i:34199
  • [HL3] A. Hinkkanen, I. Laine, Solutions of a modified fifth Painlevé equation are meromorphic, Report Univ. Jyväskylä 83 (2001), 133-146. MR 2003a:34153
  • [I] E.L. Ince, Ordinary differential equations, Dover Publ., 1956. MR 6:65f
  • [P1] P. Painlevé, Mémoire sur les équations différentielles dont l'intégrale générale est uniforme, Bull. Soc. Math. France 28 (1900), 201-261.
  • [P2] P. Painlevé, Sur les équations différentielles du second ordre et d'ordre supérieur, dont l'intégrale générale est uniforme, Acta Math. 25 (1902), 1-86.
  • [Sh] S. Shimomura, Growth of the first, the second and the fourth Painlevé transcendents, Math. Proc. Cambr. Philos. Soc. 134 (2003), 259-269. MR 2004a:34175
  • [St1] N. Steinmetz, On Painlevé's equations I, II, and IV, Journal d'Analyse Math. 82 (2000), 363-377. MR 2002d:34157
  • [St2] N. Steinmetz, Value distribution of the Painlevé transcendents, Israel J. Math. 128 (2002), 29-52. MR 2003c:34152
  • [W] H. Wittich, Eindeutige Lösungen der Differentialgleichungen $w''= P(z,w),$ Math. Ann. 125 (1953), 355-365. MR 14:873e

Review Information:

Reviewer: Norbert Steinmetz
Affiliation: University of Dortmund
Email: stein@math.uni-dortmund.de
Journal: Bull. Amer. Math. Soc. 41 (2004), 523-528
MSC (2000): Primary 34M05, 34M55, 30D35
Published electronically: March 24, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society