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 $F_n$ denotes the $n$th | + | where $F_n$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]]. |
=Properties= | =Properties= | ||
| Line 9: | Line 9: | ||
=See Also= | =See Also= | ||
| − | [[Fibonacci | + | [[Fibonacci numbers]] <br /> |
[[Reciprocal Fibonacci constant]]<br /> | [[Reciprocal Fibonacci constant]]<br /> | ||
Revision as of 00:25, 24 May 2017
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 Fibonacci number.
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 numbers
Reciprocal Fibonacci constant
