Painlev\'e Property and Generating Functions for Asymptotics
Abstract
This paper proposes a new approach to the asymptotic analysis of Painlev\'e equations. The approach is based on representing solutions of the Painlev\'e equations using formal series in two variables, Σk=0∞ykAk(x), with rational functions Ak(x). The approach is applied to the asymptotic analysis of the third degenerate Painlev\'e equation.
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