An algorithm of computing inhomogeneous differential equations for definite integrals
Mathematics - Classical Analysis and ODEs | Mathematics - Algebraic Geometry
arxiv: Mathematics::Commutative Algebra
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.