# On Positivity and Minimality for Second-Order Holonomic Sequences

@inproceedings{Kenison2021OnPA, title={On Positivity and Minimality for Second-Order Holonomic Sequences}, author={George Kenison and Oleksiy Klurman and Engel Lefaucheux and Florian Luca and Pieter Moree and Jo{\"e}l Ouaknine and Markus A. Whiteland and James Worrell}, booktitle={MFCS}, year={2021} }

An infinite sequence $\langle{u_n}\rangle_{n\in\mathbb{N}}$ of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with polynomial coefficients. Such a sequence is said to be positive if each $u_n \geq 0$, and minimal if, given any other linearly independent sequence $\langle{v_n}\rangle_{n \in\mathbb{N}}$ satisfying the same recurrence relation, the ratio $u_n/v_n$ converges to $0$. In this paper, we focus on holonomic sequences…

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