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

摘要

We present an algorithm for computing a holonomic system for a definiteintegral of a holonomic function over a domain defined by polynomialinequalities. If the integrand satisfies a holonomic difference-differentialsystem including parameters, then a holonomic difference-differential systemfor the integral can also be computed. In the algorithm, holonomicdistributions (generalized functions in the sense of L. Schwartz) areinevitably involved even if the integrand is a usual function.