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help mo on a recursive function

• To: mathgroup at smc.vnet.net
• Subject: [mg52901] help mo on a recursive function
• From: smollest at supereva.it
• Date: Thu, 16 Dec 2004 03:40:41 -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