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Math Help - [SOLVED] simple difference equation

  1. #1
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    [SOLVED] simple difference equation

    if p=q-1. and h_{k}=ph_{k+1}+qh_{k-1} and h_{1}=ph_{2}+q for k=1 than how by using difference equation theory is a G.S h_{k}=A+B(\frac{q}{p})^k? I can just about see where you get 1^k but not (\frac{q}{p})^k thanks
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  2. #2
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    Some observations

    Quote Originally Posted by oxrigby View Post
    if p=q-1. and h_{k}=ph_{k+1}+qh_{k-1} and h_{1}=ph_{2}+q for k=1
    \implies h_0 = 1


    Quote Originally Posted by oxrigby View Post
    h_{k}=A+B(\frac{q}{p})^k? I can just about see where you get 1^k but not (\frac{q}{p})^k thanks
    \implies 1 =A+B
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  3. #3
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    still makes no sense,,,why q/p?
    px^2-x+q=0
    x(px-1)+q=0
    px-1=-1+p
    implies x=1. i.e h_{k}=A.1^k<br />
how does x =q/p?
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