# Thread: Fibonacci Series Generating Function

1. ## Fibonacci Series Generating Function

The generating function of the Fibonacci series is F(x) = x / (1 - x - x^2).
The generating function of the Fibonacci series of negative numbers is F1(x) = x / (1 + x - x^2).
(Assuming f0 = 0 and f1 = 1 as starting points).

Is there any relationship or formula between F(x) and F1(x)?

2. ## Re: Fibonacci Series Generating Function

Originally Posted by RRR
The generating function of the Fibonacci series is F(x) = x / (1 - x - x^2).
The generating function of the Fibonacci series of negative numbers is F1(x) = x / (1 + x - x^2).
(Assuming f0 = 0 and f1 = 1 as starting points).

Is there any relationship or formula between F(x) and F1(x)?

Perhaps you should find $\frac{F(x)}{F_1(x)}$.