I have a system of two recursive equations with two unknowns A[n] and B[n] which apparently Mathematica can't solve
RSolve not evaluating when given my system of recurrence equations
Each $A[n]$ is a polynomial divided by a Pochhammer symbol: $A[n] = p(q)/(q)_n = p(q)/\prod_{j=1}^n (1-q^j)$ where $p(q) \in \mathbb{Z}[q]$.
I am only interested in computing the formal sum $\sum_{n \geq 0} A[n]$ as a power series in $q$. Is this something Mathematica can do? I know how to get the corresponding polynomial to each order of $n$ but I am interested in a closed formula for the formal sum.
For completeness I am copying the system of equations with initial conditions here:
RSolve[
{(1 - q^n) A[n] == q^(3 n - 1) B[n - 1] + q^(2 n + 1) A[n - 1] + q^(4 n - 2) A[n - 2] + q^(4 n - 2) B[n - 2],
B[n] == q^(n + 1) A[n - 1] - q^(5 n - 5) A[n - 3] - q^(5 n - 5) B[n - 3],
A[0] == 1, A[1] == q^3/(1 - q), A[2] == q^6/((1 - q) (1 - q^2)),
B[0] == 0, B[1] == q^2, B[2] == q^6/(1 - q)},
{A[n], B[n]}, n]
_ 2supposed to mean? Typo? – MikeY Feb 26 '20 at 17:09