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Thread: [SOLVED] simple difference equation

  1. #1
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    [SOLVED] simple difference equation

    if p=q-1. and$\displaystyle h_{k}=ph_{k+1}+qh_{k-1}$ and $\displaystyle h_{1}=ph_{2}+q$ for k=1 than how by using difference equation theory is a G.S $\displaystyle h_{k}=A+B(\frac{q}{p})^k$? I can just about see where you get$\displaystyle 1^k$ but not$\displaystyle (\frac{q}{p})^k$ 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$\displaystyle h_{k}=ph_{k+1}+qh_{k-1}$ and $\displaystyle h_{1}=ph_{2}+q$ for k=1
    $\displaystyle \implies h_0 = 1$


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