English

Explicit error term of the elliptic asymptotics for the first Painlev\'e transcendents

Classical Analysis and ODEs 2024-09-16 v2

Abstract

For the first Painlev\'e transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips near the point at infinity. We present an explicit error bound of this asymptotic expression, which leads to the order estimate of exponent 1-1.

Keywords

Cite

@article{arxiv.2307.14639,
  title  = {Explicit error term of the elliptic asymptotics for the first Painlev\'e transcendents},
  author = {Shun Shimomura},
  journal= {arXiv preprint arXiv:2307.14639},
  year   = {2024}
}