on infinite repeated function composition

Question:on infinite repeated function composition

Posted: Scimann 511 Product: Maple 13

June 04 2010

Let

G:=s->q(1-ps)^(-1)

be a generating function with 1-p=q in (0,1). Then the repeated function composition

G(G(G(s)));(G@@3)(s);simplify(%);

gives me some concrete expression. What is the simplest way to get the general expression for 3 replaced by n?

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