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

2011/08/31 by Toshinori Oaku · 2 citations
Computer Science · Mathematics · #cs.SC #math.CA

paper · pdf · doi:10.1016/j.jsc.2012.05.004

published as J. Symbolic Computation 50 (2013) 1-27 · corrected typos; Sections 5 and 6 were slightly revised with results unchanged

arxiv created 2011/10/29 · arxiv updated 2016/04/05

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.

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