Difference between revisions of "Fibonacci zeta function"
From specialfunctionswiki
| Line 1: | Line 1: | ||
The Fibonacci zeta function is defined by | The Fibonacci zeta function is defined by | ||
$$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_n^z},$$ | $$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_n^z},$$ | ||
| − | where $ | + | where $F_n$ denotes the $n$th term in the [[Fibonacci sequence]]. |
=Properties= | =Properties= | ||
Revision as of 18:49, 10 December 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 in terms of a sum of binomial coefficients
Fibonacci zeta at 1 is irrational
Fibonacci zeta is transcendental at positive even integers
See Also
Fibonacci sequence
Reciprocal Fibonacci constant
