From: Mathieu Bouchard <matju@...>
Date: 2005-03-21T20:02:38+09:00
Subject: Re: Fibonacci Benchmark Correction


On Mon, 21 Mar 2005, Martin DeMello wrote:
> Mathieu Bouchard <matju@sympatico.ca> wrote:
> > > F(i) == (f**i - F**i) / sqrt(5.0)
> > There's something else that makes the f(0)=0 series special: they have the
> > property that f(x) for even x is an even function, and f(x) for odd x is
> > an odd function.
> > This fact is quite related to the Binet formula that you state (and that I
> > quoted above).
> Huh? What precisely are f() and x in this context?

f(0)=0
f(x)=f(x-1)+f(x-2)
f(x)=f(x+2)-f(x+1) (equivalent to the previous line)

or f(x)=(a**x-b**x)/(a-b) for a,b = the z-roots of z**2-z-1

then f(-x)=((-1)**x)*f(x)
so  f(-x)=+f(x) for x=0 mod 2
and f(-x)=-f(x) for x=1 mod 2

(is that better?)

_____________________________________________________________________
Mathieu Bouchard -=- Montr�al QC Canada -=- http://artengine.ca/matju