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Math Help - Fibonacci Series Generating Function

  1. #1
    RRR
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    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)?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Fibonacci Series Generating Function

    Quote Originally Posted by RRR View Post
    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)}.
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