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Thread: Recursive function

  1. #1
    Junior Member
    Jan 2009

    Recursive function

    I'm unsure where to post this, so sorry if it's in the wrong place.

    How can I find an equation for the following function?

    $\displaystyle f(x)=f(x-1)*(g \circ f(x-1))^n -m(h \circ f(x-1))$

    Knowing that $\displaystyle f(0) = 10^4$ and that $\displaystyle g(f(t))$ and $\displaystyle r(f(t))$ are linear functions in the form $\displaystyle a*f(t) + b$.

    I've tried taking $\displaystyle f(0)$ to evaluate $\displaystyle f(1)$ and then $\displaystyle f(2)$, $\displaystyle f(3)$, etc, to try to see a pattern for $\displaystyle f(x)$, but the only thing I've got so far was:

    $\displaystyle f(x)=10^4*\prod_{i=0}^{x-1} (g \circ f(i)^n)-m\sum_{j=0}^{x-2}(r\circ f(j)*\prod_{k=j+1}^{x-1}[g \circ f(k)^n])-m(r\circ f(x-1))$

    Which is not a desired expression for the function.

    Last edited by Referos; May 20th 2009 at 02:01 PM. Reason: fixed typo
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