Fibonacci zeta function
From specialfunctionswiki
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
Theorem: The number $F(1)$ is an irrational number.
Proof: █
Theorem: The number $F(2k)$ is a transcendental number for all $k=1,2,3,\ldots$.
Proof: █
