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View all- Kauers MNuspl PPillwein V(2023)Order bounds for C2-finite sequencesProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597070(389-397)Online publication date: 24-Jul-2023
Simple C2-finite Sequences: a Computable Generalization of C-finite Sequences
Pages 45 - 53
Abstract
A sequence is called C-finite, if it satisfies a linear recurrence with constant coefficients and holonomic, if it satisfies a linear recurrence with polynomial coefficients. The class of C2-finite sequences is a natural generalization of holonomic sequences and consists of sequences satisfying a linear recurrence with C-finite coefficients whose leading coefficient has no zero terms. Recently, we investigated computational properties of $C^2$-finite sequences: we showed that these sequences form a difference ring and provided methods to compute in this ring.
From an algorithmic point of view, some of these results were not as far reaching as we hoped for. In this paper, we define the class of simple C2-finite sequences and show that it satisfies the same computational properties, but does not share the same technical issues. In particular, we are able to derive bounds for the asymptotic behavior, can compute closure properties more efficiently, and have a characterization via the generating function.
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Index Terms
- Simple C2-finite Sequences: a Computable Generalization of C-finite Sequences
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On C2-finite Sequences
ISSAC '21: Proceedings of the 2021 International Symposium on Symbolic and Algebraic ComputationHolonomic sequences are widely studied as many objects interesting to mathematicians and computer scientists are in this class. In the univariate case, these are the sequences satisfying linear recurrences with polynomial coefficients and also referred ...
An extension of holonomic sequences: C 2-finite sequences
AbstractHolonomic sequences are widely studied as many objects interesting to mathematicians and computer scientists are in this class. In the univariate case, these are the sequences satisfying linear recurrences with polynomial coefficients ...
Order bounds for C2-finite sequences
ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic ComputationA 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 C2-finite sequences satisfy similar closure ...
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Published: 05 July 2022
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View all- Kauers MNuspl PPillwein V(2023)Order bounds for C2-finite sequencesProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597070(389-397)Online publication date: 24-Jul-2023
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