PORTUGALIAEMATHEMATICA
Vol. 61, No. 3, pp. 369-374 (2004)
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PORTUGALIAE MATHEMATICA Vol. 61, No. 3, pp. 369-374 (2004) |
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Boutroux's method vs. re-scaling -- Lower estimates for the orders of growth of the second and fourth Painlevé transcendentsNorbert SteinmetzUniversität Dortmund, Fachbereich Mathematik,D-44221 Dortmund -- GERMANY E-mail: stein@math.uni-dortmund.de WWW: http://www.mathematik.uni-dortmund.de/steinmetz/ Abstract: We give a new proof of Shimomura's sharp lower estimates for the orders of growth of the Painlevé transcendents II and IV: $\varrho_{II}\ge 3/2$ and $\varrho_{IV}\ge 2$. Keywords: Painlevé differential equations; order of growth; re-scaling; Boutroux's method. Classification (MSC2000): 34M05, 30D35. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2004 Sociedade Portuguesa de Matemática
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