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<p>For the first Painlevé transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips tending along generic directions near the point at infinity. For this elliptic expression we present an explicit asymptotic formula of the error term, which leads to the error bound of exponent <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-1\)</EquationSource> </InlineEquation>.</p>

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Explicit Error Term of the Elliptic Asymptotics for the First Painlevé Transcendents

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • Shun Shimomura

摘要

For the first Painlevé transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips tending along generic directions near the point at infinity. For this elliptic expression we present an explicit asymptotic formula of the error term, which leads to the error bound of exponent \(-1\) .