Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, these input data can be analyzed in different ways, leading to vastly different precision for the extrapolation of the expansion parameter away from its original asymptotic regime. Here, we describe how conformal maps and uniformizing maps can be used, in conjunction with Padé approximants, to increase the precision of the information that can be extracted from a finite amount of perturbative input data. We also summarize results from the physical interpretation of Padé approximations in terms of electrostatic potential theory.

物理应用中的微扰扩展通常是发散的，可以使用 Borel 分析来研究它们的物理内容。仅给定有限数量的此类扩展项，可以以不同方式分析这些输入数据，从而导致扩展参数从其原始渐近状态外推的精度大不相同。在这里，我们描述了如何将保形图和统一化图与 Padé 近似值结合使用，以提高可以从有限量的微扰输入数据中提取的信息的精度。我们还总结了根据静电势理论对 Padé 近似的物理解释的结果。