N Joshi and M Mazzocco 2003 Nonlinearity 16 427 doi:10.1088/0951-7715/16/2/304
N Joshi1 and M Mazzocco2,3
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The first five classical Painlevé equations are known to have solutions described by divergent asymptotic power series near infinity. Here, we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlevé equation. Moreover, we prove that these are unique in certain sectors near infinity.
34M30 Asymptotics, summation methods
34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
Issue 2 (March 2003)
Received 29 May 2002, in final form 1 November 2002
Published 18 December 2002
N Joshi and M Mazzocco 2003 Nonlinearity 16 427
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