Type: Article

Algebraic independence of infinite products generated by Fibonacci and Lucas numbers

Luca, F; Tachiya Y.;

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 Pi(infinity)(k=1)(1+1/F-2(k)) and Pi(infinity)(k=1)(1+1/L-2(k)) are algebraically independent over Q, where {F-n}(n >= 0) and {L-n}(n >= 0) are the Fibonacci sequence and its Lucas companion, respectively.