Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers

Details Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers

2011-06-21

arxiv.org/abs/1106.4246v1

DARF 2011, AIP Conf. Proc., Sept. 6, 2011, Vol. 1385, pp. 97-100

Mathematics

Number Theory

4 pages, submitted for publication

Scientific paper

10.1063/1.3630044

In 2007, Tachiya gave necessary and sufficient conditions for the transcendence of certain infinite products involving Fibonacci numbers $F_k$ and Lucas numbers $L_k$. In the present note, we explicitly evaluate two classes of his algebraic examples. Special cases are$$\prod_{n=1}^{\infty}(1+\frac{1}{F_{2^n+1}})=\frac{3}{\phi}, \qquad \prod_{n=1}^{\infty}(1+\frac{1}{L_{2^n+1}})=3-\phi\, ,$$where $\phi=(1+\sqrt{5})/2$ is the golden ratio.

Affiliated with

Also associated with

No associations

Rating

Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-179253