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

Abstract

We present an algorithm for computing a holonomic system for a definite integral of a holonomic function 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 algorithm, holonomic distributions (generalized functions in the sense of L. Schwartz) are inevitably involved even if the integrand is a usual function.

corrected typos; Sections 5 and 6 were slightly revised with results unchanged

References in corpus (1)

• An algorithm of computing inhomogeneous differential equations for definite integrals

Cited by in corpus (3)

• Computing the volume of compact semi-algebraic sets
• Operational calculus for holonomic distributions in the framework of D-module theory
• An algorithm to compute the differential equations for the logarithm of a polynomial