Difference between revisions of "Fibonacci zeta function"
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Revision as of 03:04, 5 August 2016
The Fibonacci zeta function is defined by $$F(s)=\displaystyle\sum_{k=1}^{\infty} f_n^{-s},$$ where $f_n$ denotes the $n$th term in the Fibonacci sequence.
Properties
Fibonacci zeta at 1 is irrational
Theorem: The number $F(2k)$ is a transcendental number for all $k=1,2,3,\ldots$.
Proof: █
