Clarkson, Peter, Law, Chun-Kong, Lin, Chia-Hua (2023) A Constructive Proof for the Umemura Polynomials of the for the third Painlevé equation. Symmetry, Integrability and Geometry: Methods and Applications, 19 . Article Number 080. ISSN 1815-0659. (doi:10.3842/SIGMA.2023.080) (KAR id:103469)
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| Official URL: https://doi.org/10.3842/SIGMA.2023.080 |
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Abstract
We are concerned with the Umemura polynomials associated with rational solutions of the third Painlevé equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlevé equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation which determines the Umemura polynomials are indeed polynomials. Our proof is constructive and gives information about the roots of the Umemura polynomials.
| Item Type: | Article |
|---|---|
| DOI/Identification number: | 10.3842/SIGMA.2023.080 |
| Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations |
| Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
| Funders: | University of Kent (https://ror.org/00xkeyj56) |
| Depositing User: | Peter Clarkson |
| Date Deposited: | 27 Oct 2023 10:06 UTC |
| Last Modified: | 05 Nov 2024 13:09 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/103469 (The current URI for this page, for reference purposes) |
Available versions of this item
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A Constructive Proof for the Umemura Polynomials of the for the third Painlevé equation. (deposited 18 Jan 2017 06:21)
- A Constructive Proof for the Umemura Polynomials of the for the third Painlevé equation. (deposited 27 Oct 2023 10:06) [Currently Displayed]
University of Kent Author Information
Clarkson, Peter.
| Creator's ORCID: |
 https://orcid.org/0000-0002-8777-5284
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