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arXiv · 2512.14970

Painlev\'{e} Property and Generating Functions for Asymptotics

A. V. Kitaev
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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, $\sum_{k=0}^{\infty}y^kA_k(x)$, with rational functions $A_k(x)$. The approach is applied to the asymptotic analysis of the third degenerate Painlev\'e equation.

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A. V. Kitaev. 2025-12-16. Painlev\'{e} Property and Generating Functions for Asymptotics. https://arxiv.org/abs/2512.14970

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