Difference between revisions of "Fibonacci zeta function"
From specialfunctionswiki
| Line 13: | Line 13: | ||
=References= | =References= | ||
| − | * {{PaperReference|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Fibonacci | + | * {{PaperReference|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Fibonacci numbers|next=Binet's formula}} |
[http://cc.oulu.fi/~tma/TAPANI20.pdf]<br /> | [http://cc.oulu.fi/~tma/TAPANI20.pdf]<br /> | ||
[http://www.fq.math.ca/Scanned/39-5/navas.pdf]<br /> | [http://www.fq.math.ca/Scanned/39-5/navas.pdf]<br /> | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest 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
