Singularities of the First Painlev{\'{e}} Transcendent
Classical Analysis and ODEs
2026-03-02 v1
Abstract
Consider the solution for the ordinary differential equation with complex. Second-order nonlinear differential equations often exhibit patterns in their poles, branch points, and essential singularities, explored by \Pain and colleagues, 1888--1915. A variant of the ratio test applied to the Taylor series for the solution estimates the locations and orders of singularities in the First Painlev{\'{e}} Transcendent as an example. Can you suggest applications in which our singularity location analysis can provide useful insights?
Cite
@article{arxiv.2602.23483,
title = {Singularities of the First Painlev{\'{e}} Transcendent},
author = {George F. Corliss},
journal= {arXiv preprint arXiv:2602.23483},
year = {2026}
}