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Main Author: Corliss, George F.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.23483
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author Corliss, George F.
author_facet Corliss, George F.
contents Consider the solution $y(t)$ for the ordinary differential equation $y' = f(t, y)$ with $t$ 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 $y$ estimates the locations and orders of singularities in the First Painlev{é} Transcendent as an example. Can you suggest applications in which our singularity location analysis can provide useful insights?
format Preprint
id arxiv_https___arxiv_org_abs_2602_23483
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Singularities of the First Painlev{é} Transcendent
Corliss, George F.
Classical Analysis and ODEs
65L05
G.1
Consider the solution $y(t)$ for the ordinary differential equation $y' = f(t, y)$ with $t$ 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 $y$ estimates the locations and orders of singularities in the First Painlev{é} Transcendent as an example. Can you suggest applications in which our singularity location analysis can provide useful insights?
title Singularities of the First Painlev{é} Transcendent
topic Classical Analysis and ODEs
65L05
G.1
url https://arxiv.org/abs/2602.23483