Hone, Andrew N.W., Ragnisco, Orlando, Zullo, Federico (2013) Properties of the series solution for Painlevé I. Journal of Nonlinear Mathematical Physics, 20 (Supp.1). pp. 85100. ISSN 14029251. (doi:10.1080/14029251.2013.862436) (KAR id:41485)
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Official URL http://dx.doi.org/10.1080/14029251.2013.862436 
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 taufunction 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.
Item Type:  Article 

DOI/Identification number:  10.1080/14029251.2013.862436 
Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA351 Special functions Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations 
Divisions:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science 
Depositing User:  Andrew Hone 
Date Deposited:  20 Jun 2014 23:34 UTC 
Last Modified:  06 Feb 2020 04:09 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/41485 (The current URI for this page, for reference purposes) 
Hone, Andrew N.W.:  https://orcid.org/0000000197807369 
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