Properties of the series solution for Painlevé I
- 10.1080/14029251.2013.862436How to use a DOI?
- Painlevé equation; tau-function; sigma function
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.
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
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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 -