The power expansions of the solutions of the first painlevé hierarchy

Abstract

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.

Key words:

• Painlevé equation
• P‐type equations
• power expansions
• power geometry