揭示隐藏模式：基于截断级数的近似复兴重求和
Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series
AI总结：
针对非线性一阶常微分方程的发散截断级数，本文结合 Borel-Padé 近似与经典分析提取解析结构，并构建符合复兴性质的近似式，以获得可实用的 Borel-Ecalle 重求和。
摘要：
我们分析了由非线性常微分方程的发散形式解所生成的截断级数。推动本研究的是一个特定的非线性一阶微分方程，它是量子场论中重整化微扰理论复兴表述的基础。我们利用 Borel-Padé 近似式和经典分析，仅借助解的渐近级数的前几项来确定解的解析结构。随后，我们构建了一个与该方程的复兴性质相一致的近似式。该过程给出了解的 Borel-Ecalle 重求和的近似表达式，可用于实际应用。文中还讨论了与其他物理应用的联系。
英文摘要：
We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent formulation of renormalized perturbation theory in quantum field theory. We use the Borel-Padé approximant and classical analysis to determine the analytic structure of the solution using the first few terms of its asymptotic series. Afterward, we build an approximant, consistent with the resurgent properties of the equation. The procedure gives an approximate expression for the Borel-Ecalle resummation of the solution useful for practical applications. Connections with other physical applications are also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
