uniqueness of fibonacci number extension
- From: bo198214 <bo198214@xxxxxxxxxxxxxx>
- Date: Mon, 5 May 2008 01:30:01 +0000 (UTC)
We know that there is a closed form for the Fibonacci function
(1) F(n)=F(n-1)+F(n-2), F(0)=0, F(1)=1
given by
F(n)=(r^n+(1-r)^n)/sqrt(5), where r=(1+sqrt(5))/2
Actually this is an extension from the domain of definition being the
natural numbers to real or even complex numbers. The extension is
analytic and satisfies equations (1) for all complex n.
My question:
Are there research results which give conditions that makes this
extension unique under all analytic extensions that also satisfy
equations (1) for all complex n? Or is this extension already unique
be these requirements?
.
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