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 $f_n$ denotes the $n$th term in the [[Fibonacci sequence]].
+
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 zeta in terms of a sum of binomial coefficients]]<br />
+
 
 +
=See Also=
 +
[[Fibonacci numbers]] <br />
 +
[[Reciprocal Fibonacci constant]]<br />
  
 
=References=
 
=References=
* {{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 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

References

[1]
[2]