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

摘要

A holonomic function is a differentiabte or generalized function which satisfies a hofortomic system of linear partial or ordinary differential equations with polynomial coefficients. The main purpose of this paper is to present algorithms for computing a holonomic system for the definite integral of a holonomic function with parameters over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including parameters, then a holonomic difference-differential system for the integral can also be computed. In the algorithms, holonomic distributions (generalized functions in the sense of L. Schwartz) are inevitably involved even if the integrand is a usual function.