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Math Help - [SOLVED] Maple - HELP PLEASE!

  1. #1
    maplemaple
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    [SOLVED] Maple - HELP PLEASE!

    How can I write an algorithm in maple that gives me a lisft of the Fibonacci polynomies between two numbers using the recursion:

    F1(x) = 1
    F2(x) = x
    Fn+1(x) = x*Fn(x) + Fn−1(x)

    if anyone knows please help me!!
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Yes, it's the rsolve command.

    i.e., to generate the closed-form for the nth Fibonacci number type:

    rsolve({f(n)=f(n-1)+f(n-2),f(0)=1,f(1)=1},{f(n)});

    This will give you:

    f(n)=(\frac{1}{2}+\frac{1}{10}\sqrt{5})(\frac{1}{2  }\sqrt{5}+\frac{1}{2})^{n}+(\frac{1}{2}-\frac{1}{10}\sqrt{5})(\frac{-1}{2}\sqrt{5}+\frac{1}{2})^{n}

    Which is the formula we get from Binet's formula.

    By tweaking it accordingly, you should get the polynomials:

    x+x^{2}+2x^{3}+3x^{4}+5x^{5}+..........

    The closed-form is \boxed{\frac{x}{1-x-x^{2}}}
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