Open AccessTHE POWER EXPANSIONS OF THE SOLUTIONS OF THE FIRST PAINLEVÉ HIERARCHY
Author(s) -
A. A. Grigor'ev,
V. I. Gromak
Publication year - 2006
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2006.9637326
Subject(s) - holomorphic function , hierarchy , mathematics , order (exchange) , power (physics) , pure mathematics , mathematical analysis , physics , law , finance , quantum mechanics , economics , political science
In this paper we consider a hierarchy of the first Painlevé equation's higher order analogues. For these equations three types of power expansions, i.e. holomorphic, polar and asymptotic are found. As an example the equation of the fourth order is considered.