Creative Telescoping for Holonomic Functions

@article{Koutschan2013CreativeTF,
  title={Creative Telescoping for Holonomic Functions},
  author={Christoph Koutschan},
  journal={ArXiv},
  year={2013},
  volume={abs/1307.4554}
}
The aim of this article is twofold: on the one hand it is intended to serve as a gentle introduction to the topic of creative telescoping, from a practical point of view; for this purpose its application to several problems is exemplified. On the other hand, this chapter has the flavour of a survey article: the developments in this area during the last two decades are sketched and a selection of references is compiled in order to highlight the impact of creative telescoping in numerous contexts… 
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References

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TLDR
This note reinvestigate the task of computing creative telescoping relations in differential–difference operator algebras using an ansatz that explicitly includes the denominators of the delta parts and shows that it can be superior to existing methods by a large factor.
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TLDR
This work describes a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of rational functions that leads to bounds on the order and degree of the coefficients of the differential equation, and to the first complexity result which is single exponential in the number of variables.
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TLDR
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TLDR
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TLDR
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TLDR
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