Abstract
The first and second Painlevé equation hierarchies are considered. The relations between them are given. The Bäcklund transformations for the second Painlevé equations of higher order are presented. Some rational solutions of these equations are obtained. The indices for the first and second Painlevé equations of fourth order are found. These equations are shown to pass the Painlevé test. Lax pairs for the first and second Painlevé equations of higher order are given. The transcendence of the solutions for the first Painlevé hierarchy is discussed.
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