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February 2014 Algebraic independence of infinite products generated by Fibonacci and Lucas numbers
Florian LUCA, Yohei TACHIYA
Hokkaido Math. J. 43(1): 1-20 (February 2014). DOI: 10.14492/hokmj/1392906090

Abstract

The aim of this paper is to give an algebraic independence result for the two infinite products involving the Lucas sequences of the first and second kind. As a consequence, we derive that the two infinite products ∏k=1(1+1/F2k) and ∏k=1(1+1/L2k) are algebraically independent over ℚ, where {Fn}n≥0 and {Ln}n≥0 are the Fibonacci sequence and its Lucas companion, respectively.

Citation

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Florian LUCA. Yohei TACHIYA. "Algebraic independence of infinite products generated by Fibonacci and Lucas numbers." Hokkaido Math. J. 43 (1) 1 - 20, February 2014. https://doi.org/10.14492/hokmj/1392906090

Information

Published: February 2014
First available in Project Euclid: 20 February 2014

zbMATH: 1291.11103
MathSciNet: MR3072299
Digital Object Identifier: 10.14492/hokmj/1392906090

Subjects:
Primary: 11B39, 11J85

Rights: Copyright © 2014 Hokkaido University, Department of Mathematics

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Vol.43 • No. 1 • February 2014
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