[bib]

@**inproceedings**{RISC6751,

author = {M. Kauers and P. Nuspl and V. Pillwein},

title = {{Order bounds for $C^2$-finite sequences}},

booktitle = {{Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation}},

language = {english},

abstract = {A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences satisfy similar closure properties as $C$-finite sequences. In particular, they form a difference ring. In this paper we present new techniques for performing these closure properties of $C^2$-finite sequences. These methods also allow us to derive order bounds which were not known before. Additionally, they provide more insight in the effectiveness of these computations. The results are based on the exponent lattice of algebraic numbers. We present an iterative algorithm which can be used to compute bases of such lattices.},

series = {ISSAC '23, Tromso{}, Norway},

pages = {389--397},

publisher = {Association for Computing Machinery},

address = {New York, NY, USA},

isbn_issn = {9798400700392}},

year = {2023},

month = {July},

editor = {A.Dickenstein and E. Tsigaridas and G. Jeronimo},

refereed = {no},

keywords = {Difference equations, holonomic sequences, closure properties, algorithms},

length = {9},

url = {https://doi.org/10.35011/risc.23-03}

}