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：费曼积分是具有多项式系数的线性偏微分方程的解。以一般指数下的三角形积分为例，我们将$D$-模方法与为求解费曼积分中出现的微分方程而开发的专用方法进行比较，并提供相关概念的对照表。特别地，我们实现了Saito、Sturmfels和Takayama的算法，推导出正则完整$D$-理想的典型级数解，并将其与通过相应Fuchs系统得到的渐近级数进行比较。