Volume 20, Issue Supplement 1, November 2013, Pages 85 - 100
Properties of the series solution for Painlevé I
Authors
A.N.W. Hone
School of Mathematics, Statistics & Actuarial Science, University of Kent Canterbury, Kent, U.K.A.N.W.Hone@kent.ac.uk
O. Ragnisco, F. Zullo
Dipartimento di Fisica, Università Roma Tre, Via della Vasca Navale 84 Roma, Italy,ragnisco@fis.uniroma3.it,zullo@fis.uniroma3.it
Received 2 October 2012, Accepted 20 June 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.862436How to use a DOI?
- Keywords
- Painlevé equation; tau-function; sigma function
- Abstract
We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painlevé equation. For the general solution, explicit recursive formulae for the Taylor expansion of the tau-function around a zero are given, which are natural extensions of analogous formulae for the elliptic sigma function, as given by Weierstrass. Numerical and exact results on the symmetric solution which is singular at the origin are also presented.
- Copyright
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - A.N.W. Hone AU - O. Ragnisco AU - F. Zullo PY - 2021 DA - 2021/01/06 TI - Properties of the series solution for Painlevé I JO - Journal of Nonlinear Mathematical Physics SP - 85 EP - 100 VL - 20 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.862436 DO - 10.1080/14029251.2013.862436 ID - Hone2021 ER -