Operational calculus for holonomic distributions in the framework of D-module theory

Abstract

Let $f$ be a real polynomial of $x=(x_1,\dots ,x_n)$ and $\phi$ be a locally integrable function of $x$ which satisfies a holonomic system of linear differential equations. We study the distribution $f_{+}^{\lambda }\phi$ with a meromorphic parameter $\lambda$, especially its Laurent expansion and integration, from an algorithmic viewpoint in the framework of $D$-module theory.

19 pages

References in corpus (1)

• Algorithms for integrals of holonomic functions over domains defined by polynomial inequalities