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!