Using rsolve in Maple

Question

I have tried using rsolve in Maple to obtain a recursion formula from an ordinary differential equation with summations.

I get

Is there some reason for Maple not calculating the sums?

It seems rsolve is not used at all; however, it seems to work if I don't use sums in $x(t)$ and $u(t)$.

I am not sure if this questions belongs to stackoverflow or math.stackexchange.com, so please tell me if I should close the question.

Thanks.

Answer 1

Maple will only solve recurrence relations that it recognizes as such. What you have is a specification for a recurrence. You need to actually extract it yourself before handing it over.

In this particular case, the recurrence is

zz := 3*(n+1)*c(n+1)*t^n + 2*c(n)*t^n-d(n)*t^n;

which Maples solves via

rsolve(zz, c(n));

as

-3^(-n)*(-1)^n*(2^(n-1)*(sum(3^n1*d(n1)*GAMMA(n1)*n1*(-1)^(-n1)*2^(-n1), n1 = 0 .. n-1))-2^n*c(0))/GAMMA(n+1)

(I am pasting in the Maple, as that is more useful than the 'pretty' version, IMHO).