Extension of a theorem of Duffin and Schaeffer

Title: Extension of a theorem of Duffin and Schaeffer
Creator: Coons, Michael
Relation: Journal of Integer Sequences Vol. 20, no. 17.9.4
Relation: https://cs.uwaterloo.ca/journals/JIS/VOL20/Coons/coons7.html
Publisher: University of Waterloo
Resource Type: journal article
Date: 2017
Description: Let r₁,..., r_s: Z_n≥0 → C be linearly recurrent sequences whose associated eigenvalues have arguments in πQ and let F(z) := Σ_n ≥ 0 f(n)zn, where f(n) ∈ {r1(n),..., rs(n)} for each n ≥ 0. We prove that if F(z) is bounded in a sector of its disk of convergence, then it is a rational function. This extends a very recent result of Tang and Wang, who gave the analogous result when the sequence f(n) takes on values of finitely many polynomials.
Subject: linearly recurrent sequences; eigenvalues and eigenfunctions; polynomials
Identifier: http://hdl.handle.net/1959.13/1352561
Identifier: uon:30912
Identifier: ISSN:1530-7638
Language: eng
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