Re: Recurrence Relation Question

I wrote,

The actual recursions have been generated by successively assuming that in
example 1 P and Q are linear in X, example 2 they are quadratic in X,
example 2 cubic in X etc. and solving for their coefficients assuming that
we successively get more terms from the sequence of the Large Schroeder
numbers in the F_i's.

and "Proginoskes" <CCHeckman@xxxxxxxxx> replied

Well, if you don't, then your assumption is probably wrong.

The point is I'm not expecting to get the full sequence out for any one of
these recurrances, but successively better approximations to the sequence's
ordinary generating function. The reason we are allowed to think in these
terms is that each of these recursions defines (in the limit) a unique power
series. The reason for this is that successive terms in each F_i get
'carried down' into F_i+1. For instance, we start with F_1 = 1, and the
constant term in F_2, F_3, ... is always 1. Similarly the term in X in F_2
is the same as that in F_i for i>2, and the term in X^2 in F_3 is that in
F_i for i>3 and so on. Knowing this information it makes sense to ask how
good an approximation can I get if P and Q are linear, quadratic, cubic etc
in X.

Regards,
Eric


.

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