Difference between revisions of "Fibonacci zeta function"

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=Properties=
 
=Properties=
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[[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 />
 
  
 
=References=
 
=References=

Revision as of 13:00, 11 August 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

References

[1]