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Math Help - Finding fixed numbers

  1. #1
    Junior Member
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    Finding fixed numbers

    For a fixed number a define  \Delta_{a} x_{n} = x_{n+1} - ax_n. Find formula for  \Delta^{2}_{a}x_{n} and \Delta^{3}_{a}x_{n}. Express \Delta_{a}x_{n} in terms of \Delta x_n and x_n.

    Am I suppose to find the derivative??? I'm confused.
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  2. #2
    MHF Contributor chisigma's Avatar
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    From the definition...

    \Delta_{a} x_{n} = x_{n+1} - a\cdot x_{n} (1)

    ... follows...

    \Delta x_{n} = x_{n+1} - x_{n} = \Delta_{a}x_{n} + (a-1)\cdot x_{n} (2)

    \Delta_{a}^{2} x_{n} and \Delta_{a}^{3} x_{n} can also be derived from (1)

    Kind regards

    \chi \sigma
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