New Viète-like infinite products of nested radicals with Fibonacci and Lucas numbers
In a 2007 contribution by Osier in this Quarterly, the so-named Vieta-like products were introduced as two eye-catching formulas representing either the nth Fibonacci number in terms of a product of nested radicals with the nth Lucas number inside, or vice-versa. As the original and famous Vièete's infinite product, Osier's infinite products have plus signs inside the nested radicals. In this paper we explore infinite products of nested square roots with Fibonacci and Lucas numbers with the novelty that inside the radical symbols there are minus signs instead of plus signs.
Original Publication Date
García-Caballero, Esther M.; Moreno, Samuel G.; and Prophet, Michael P., "New Viète-like infinite products of nested radicals with Fibonacci and Lucas numbers" (2014). Faculty Publications. 1507.