Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as a case in point, we compare $D$-module methods to dedicated methods developed for solving differential equations appearing in the context of Feynman integrals, and provide a dictionary of the relevant concepts. In particular, we implement an algorithm due to Saito, Sturmfels, and Takayama to derive canonical series solutions of regular holonomic $D$-ideals, and compare them to asymptotic series derived by the respective Fuchsian systems.

翻译：在 Feynman 积分的背景下解微分方程的 $D$ 模技术 翻译后的摘要： Feynman 积分是多项式系数的线性偏微分方程的解。以一般指数的三角形积分为例，我们比较了 $D$ 模方法和针对出现在 Feynman 积分背景下的微分方程所开发的专用方法，并提供了相关概念的对照表。特别地，我们采用 Saito、Sturmfels 和 Takayama 提出的算法，导出正则全纯 $D$ 理想的规范级数解，并将其与相应的 Fuchsian 系统推导出的渐近级数进行比较。