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I have the following equation:

$(aq^n+b+s)C_n(s)=aq^nC_{n+1}(s)+bC_{n-1}(s)$ , for $n\geq1$.

$C_0(s)=1$ , and for all $s\geq 0$ we have $0\leq C_n(s)\leq1$.

$a>0$, $b>0$, $0\leq q\leq1$.

In fact, $C_n(s)$ is a Laplace Transform of a non-negative RV, for all n.

Any thoughts on how to solve this equation?

Thanks!

  • 1
    Try let $C_n(s)=\int_{-\infty}^\infty q^{nt}K(t,s)~dt$ or let $C_n(s)=\sum_{-\infty}^\infty q^{nt}K(t,s)$ .2012-09-06

1 Answers 1