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 | ||
$$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_n^z},$$ | $$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_n^z},$$ | ||
| − | where $ | + | where $F_n$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]]. |
=Properties= | =Properties= | ||
| + | [[Fibonacci zeta in terms of a sum of binomial coefficients]]<br /> | ||
[[Fibonacci zeta at 1 is irrational]]<br /> | [[Fibonacci zeta at 1 is irrational]]<br /> | ||
[[Fibonacci zeta is transcendental at positive even integers]]<br /> | [[Fibonacci zeta is transcendental at positive even integers]]<br /> | ||
| − | [[Fibonacci | + | |
| + | =See Also= | ||
| + | [[Fibonacci numbers]] <br /> | ||
| + | [[Reciprocal Fibonacci constant]]<br /> | ||
=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 /> | ||
[[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
