help on a recursive function

*To*: mathgroup at smc.vnet.net*Subject*: [mg52903] help on a recursive function*From*: Smoll Est <smollest at supereva.it>*Date*: Thu, 16 Dec 2004 03:40:47 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I'm interested on the behaviour on a H-length circular queue, empty before i=0, equal to P(0)=a and P(i)= b Sum(j=i-1, i-H [P(j)]), that is: P(i) = a(1+b)^i i=0, ..., H-1 P(i) = (1+b)P(i-1) - b P(i-H) i>= H I got just the following results: P(i) = a (b(i+1) - 1)/(b - 1) *if H=1* and lim(i->Inf [ P(i) ]) = 1 / (1-b) for each H, if | b | <1 my question is: is it possible to express this function in closed form for each H? thank you in advance, smoll-est