Constructing reductions for creative telescoping

The general differentially finite case

Abstract

The class of reduction-based algorithms was introduced recently as a new approach towards creative telescoping. Starting with Hermite reduction of rational functions, various reductions have been introduced for increasingly large classes of holonomic functions. In this paper we show how to construct reductions for general holonomic functions, in the purely differential setting.

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Acknowledgements

We would like to thank Pierre Lairez for a helpful remark. We also thank the second referee for pointing us to [18] and for further helpful remarks and suggestions.

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Correspondence to Joris van der Hoeven.

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The original version of this document has written using GNU \(\hbox{\TeX}_\mathrm{MACS}\) [20].

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van der Hoeven, J. Constructing reductions for creative telescoping. AAECC (2020). https://doi.org/10.1007/s00200-020-00413-3

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Keywords

  • Creative telescoping
  • Holonomic function
  • Hermite reduction
  • Residues

Mathematics Subject Classification

  • 33F10
  • 68W30