Difference between revisions of "Fibonacci zeta function"
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The Fibonacci zeta function is defined by | The Fibonacci zeta function is defined by | ||
| − | $$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{ | + | $$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_n^z},$$ |
where $f_n$ denotes the $n$th term in the [[Fibonacci sequence]]. | where $f_n$ denotes the $n$th term in the [[Fibonacci sequence]]. | ||
Revision as of 12:34, 10 August 2016
The Fibonacci zeta function is defined by $$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
