Properties of the series solution for Painlevé I
| العنوان: | Properties of the series solution for Painlevé I |
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| المؤلفون: | Andrew N.W. Hone, Orlando Ragnisco, Federico Zullo |
| المساهمون: | Hone, Anw, Ragnisco, Orlando, Zullo, F. |
| المصدر: | Journal of Nonlinear Mathematical Physics. 20:85 |
| بيانات النشر: | Springer Science and Business Media LLC, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | sigma function, Laurent series, FOS: Physical sciences, Painlevé equation, 01 natural sciences, symbols.namesake, QA372, 0103 physical sciences, QA351, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Taylor series, QA299, Applied mathematics, Ramanujan tau function, 0101 mathematics, Sigma function, Mathematical Physics, Mathematics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Series (mathematics), 010102 general mathematics, Zero (complex analysis), Sigma, Statistical and Nonlinear Physics, Tau-function, Function (mathematics), Painleve equation, Exact results, Mathematics - Classical Analysis and ODEs, symbols, 010307 mathematical physics, Exactly Solvable and Integrable Systems (nlin.SI), tau function |
| الوصف: | We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painleve 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. Comment: 17 pages, 1 figure. Typos corrected and additional references added |
| وصف الملف: | application/pdf |
| تدمد: | 1776-0852 1402-9251 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::038c9932075f77278682fadf8df3b796 https://doi.org/10.1080/14029251.2013.862436 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....038c9932075f77278682fadf8df3b796 |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 17760852 14029251 |
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