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：费曼积分是带有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，我们将$D$-模方法与专为解决费曼积分背景下出现的微分方程而开发的方法进行比较，并提供了相关概念对照表。特别地，我们实现了Saito、Sturmfels和Takayama的算法，用于推导正则完整$D$-理想的规范级数解，并将其与由相应Fuchs系统导出的渐近级数进行比较。