Difference between revisions of "Fibonacci zeta function"
From specialfunctionswiki
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| − | [http://www.mast.queensu.ca/~murty/fibon-tifr.pdf The Fibonacci zeta function by M. Ram Murty] | + | [http://www.mast.queensu.ca/~murty/fibon-tifr.pdf The Fibonacci zeta function by M. Ram Murty]<br /> |
| + | [http://cc.oulu.fi/~tma/TAPANI20.pdf]<br /> | ||
Revision as of 18:31, 25 July 2015
The Fibonacci zeta function is defined by $$F(s)=\displaystyle\sum_{k=1}^{\infty} f_n^{-s},$$ where $f_n$ denotes the $n$th term in the Fibonacci sequence.
Properties
Theorem: The number $F(1)$ is an irrational number.
Proof: █
Theorem: The number $F(2k)$ is a transcendental number for all $k=1,2,3,\ldots$.
Proof: █
