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

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

2011-08-24

arxiv.org/abs/1108.4853v2

Computer Science

Symbolic Computation

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

Scientific paper

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.

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