A complete view of Viète-like infinite products with Fibonacci and Lucas numbers

The main goal of this paper is to link the nth Fibonacci and Lucas numbers through certain infinite products of nested radicals. This work relies on recent results on Viète-like infinite products appeared in Moreno and García-Caballero (2013) [3]. We will analyze in detail one particular case of these formulas and we will show how our treatment covers and extends previous results in the literature.