Difference between revisions of "Fibonacci zeta function"
From specialfunctionswiki
| (13 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
The Fibonacci zeta function is defined by | The Fibonacci zeta function is defined by | ||
| − | $$F( | + | $$F(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{F_n^z},$$ |
| − | where $ | + | where $F_n$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]]. |
=Properties= | =Properties= | ||
| − | < | + | [[Fibonacci zeta in terms of a sum of binomial coefficients]]<br /> |
| − | + | [[Fibonacci zeta at 1 is irrational]]<br /> | |
| − | + | [[Fibonacci zeta is transcendental at positive even integers]]<br /> | |
| − | |||
| − | |||
| − | </ | ||
| − | + | =See Also= | |
| − | + | [[Fibonacci numbers]] <br /> | |
| − | + | [[Reciprocal Fibonacci constant]]<br /> | |
| − | |||
| − | |||
| − | </ | ||
=References= | =References= | ||
| − | + | * {{PaperReference|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Fibonacci numbers|next=Binet's formula}} | |
[http://cc.oulu.fi/~tma/TAPANI20.pdf]<br /> | [http://cc.oulu.fi/~tma/TAPANI20.pdf]<br /> | ||
| + | [http://www.fq.math.ca/Scanned/39-5/navas.pdf]<br /> | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 00:25, 24 May 2017
The Fibonacci zeta function is defined by $$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
