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
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
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