Fibonacci zeta function
From specialfunctionswiki
The Fibonacci zeta function is defined by $$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_n^z},$$ where $f_n$ denotes the $n$th term in the Fibonacci sequence.
Properties
Fibonacci zeta at 1 is irrational
Fibonacci zeta is transcendental at positive even integers
Fibonacci zeta in terms of a sum of binomial coefficients
