Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
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 transcendents

Norbert Steinmetz

Universität 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.

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Electronic version published on: 7 Mar 2008.

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