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Math Help - Generating function help plz

  1. #1
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    Generating function help plz

    Hi, I am encountering this problem:

    Let a0, a1, a2.... be an infinite sequence of non-negative integers and A(x) = the summation of an * x^n is the corresponding generating function.

    Express the following sequences in terms of A(x), and it should not contain a summation symbol or an infinite sum:
    c) a0, 0, a2, 0 , a4, 0, a6.........
    d) a0, 2a1, 4a2, 8a3, 16a4........

    I have thought so hard but still nothing come out form my mind. thanks in advance.
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  2. #2
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    for part d), is it just A(2x) ? This is also the expression in terms of A(x), right?
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  3. #3
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    Hello,

    You are right. For (c), compute A(-x).

    Bye.
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  4. #4
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by jmmjm View Post
    Hi, I am encountering this problem:

    Let a0, a1, a2.... be an infinite sequence of non-negative integers and A(x) = the summation of an * x^n is the corresponding generating function.

    Express the following sequences in terms of A(x), and it should not contain a summation symbol or an infinite sum:
    c) a0, 0, a2, 0 , a4, 0, a6.........
    d) a0, 2a1, 4a2, 8a3, 16a4........

    I have thought so hard but still nothing come out form my mind. thanks in advance.
    Do you mean A(x)=\bigg(\sum\limits_{i=0}^{n}a_{i}\bigg)x^{n}?
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  5. #5
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    Hello,

    No, I replied thinking that jmmjm meant A(x)=\sum_{n=0}^{\infty}a_nx^n.

    Bye.
    Last edited by wisterville; September 25th 2008 at 07:21 AM. Reason: Typo: summation began with n=0...
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