Difference between revisions of "Fibonacci zeta function"
From specialfunctionswiki
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=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 /> | ||
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=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
