Talk:Fibonacci polynomials

Closed Form

This is something I discovered on my own a while back, but was unable to find much info about it online. I strongly believe that it is the closed form of the Fibonacci polynomials. I arrived at it by manipulating Binet's formula with the golden function.

I used the Wikipedia math generator to create an image for a school paper, and figured it would be a dumb idea to let the code to go to waste, so here it is:

F_{n}\left(x\right)={{gold(n)^{x}-(n-gold(n))^{x}} \over {\sqrt {n^{2}+4}}}={{gold(n)^{x}-(-gold(n))^{-x}} \over {\sqrt {n^{2}+4}}}\

Again, I have no sources to verify/mathematically prove this, so I'm just posting it here instead. Enjoy!

--HeroofTime55 (talk) 05:56, 29 February 2008 (UTC)[reply]

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the summation on the left hand side for the generating functions are over m, while inside the sum they are over n. I think this is a mistake. I can't think how it could possibly be correct! —Preceding unsigned comment added by 121.45.141.190 (talk) 13:30, 21 August 2008 (UTC)[reply]

Formula in Definition

Has anybody noticed that the case for $n=2$ actually agrees with the case for $n\geq 3$ ? I'll modify the formula to reflect this; if anyone has any qualms, feel free to address them here. --JB Adder | Talk 01:11, 23 September 2008 (UTC)[reply]