Difference between revisions of "Fibonacci zeta function"
From specialfunctionswiki
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* {{PaperReference|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Fibonacci sequence|next=Binet's formula}} | * {{PaperReference|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Fibonacci sequence|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 /> | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 10:00, 13 October 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
