An algorithm of computing inhomogeneous differential equations for definite integrals

Preprint English OPEN
Nakayama, Hiromasa ; Nishiyama, Kenta (2010)
  • Subject: Mathematics - Classical Analysis and ODEs | Mathematics - Algebraic Geometry
    arxiv: Mathematics::Commutative Algebra
    acm: ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION

We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\"obner basis method in the ring of differential operators.
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