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An Algorithm of Computing Inhomogeneous Differential Equations for Definite Integrals

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6327)

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 Gröbner basis method in the ring of differential operators.

Keywords

  • integration algorithm
  • holonomic functions
  • D-module
  • Gröbner basis

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Nakayama, H., Nishiyama, K. (2010). An Algorithm of Computing Inhomogeneous Differential Equations for Definite Integrals. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_39

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  • DOI: https://doi.org/10.1007/978-3-642-15582-6_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)