Singularities of the First Painlev{é} Transcendent
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908855251763200 |
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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 |