publication . Preprint . Part of book or chapter of book . 2010

An Algorithm of Computing Inhomogeneous Differential Equations for Definite Integrals

Hiromasa Nakayama; Kenta Nishiyama;
Open Access English
  • Published: 19 May 2010
Abstract
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.
Subjects
arXiv: Mathematics::Commutative Algebra
ACM Computing Classification System: ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
free text keywords: Mathematics - Algebraic Geometry, Mathematics - Classical Analysis and ODEs, Algebraic differential equation, Algebra, Differential equation, Definite integrals, Differential operator, Discrete mathematics, Algorithm, Integration algorithm, Gröbner basis, D-module, Mathematics
Related Organizations
Download fromView all 2 versions
http://arxiv.org/pdf/1005.3417...
Part of book or chapter of book
Provider: UnpayWall
http://link.springer.com/conte...
Part of book or chapter of book
Provider: Crossref

[1] G.Almkvist, D.Zeilberger, The method of differentiating under the integral sign, Journal of Symbolic Computation 10, 571-591, 1990. [OpenAIRE]

[2] M.Apagodu, D.Zeilberger, Multi-variable Zeilberger and AlmkvistZeilberger algorithms and the sharpening of Wilf-Zeilberger theory, Advances in Applied Mathematics 37, 139-152, 2006. [OpenAIRE]

[3] F.Chyzak, Gr¨obner Bases, Symbolic Summation and Symbolic Integration, London Mathematics Lecture Notes Series, vol.251, 32-60, 1998.

[4] F.Chyzak, An Extension of Zeilberger's Fast Algorithm to General Holonomic Functions, Discrete Mathematics 217, 115-134, 2000. [OpenAIRE]

[5] F.Chyzak, B. Salvy, Non-commutative Elimination in Ore Algebras Proves Multivariate Holonomic Identities, Journal of Symbolic Computation 26, 187-227, 1998.

[6] T.Oaku, Algorithms for b-functions, restrictions, and algebraic local cohomology groups of D-modules, Advances in Applied Mathematics 19, 61-105, 1997. [OpenAIRE]

[7] T.Oaku, Y.Shiraki, and N.Takayama, Algebraic Algorithm for D-modules and numerical analysis, Computer mathematics (Proceedings of ASCM 2003), 23-39, Lecture Notes Ser. Comput., 10, World Sci. Publ., River Edge, NJ, 2003.

[8] M.Saito, B.Sturmfels, and N.Takayama, Gr¨obner Deformations of Hypergeometric Differential Equations, Springer, 2000.

[9] N.Takayama, An Approach to the Zero Recognition Problem by Buchberger Algorithm, Journal of Symbolic Computation 14, 265-282, 1992. [OpenAIRE]

[10] A.Tefera, MultInt, a Maple package for multiple integration by the WZ method, Journal of Symbolic Computation 34, 329-353, 2002. [OpenAIRE]

[11] M.Noro, et al: Risa/Asir, http://www.math.kobe-u.ac.jp/Asir

[12] F.Chyzak: Mgfun, http://algo.inria.fr/chyzak/mgfun.html

[13] C.Koutschan: HolonomicFunctions, http://www.risc.jku.at/research/combinat/software/HolonomicFunctions/

[14] H.Nakayama, K.Nishiyama: nk restriction.rr, http://www.math.kobe-u.ac.jp/~nakayama/nk restriction.rr

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Part of book or chapter of book . 2010

An Algorithm of Computing Inhomogeneous Differential Equations for Definite Integrals

Hiromasa Nakayama; Kenta Nishiyama;