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Take the following definitions:

rho = Cos[(2 Pi)/7] + I Sin[(2 Pi)/7]

F[y, q] = 
 y^3*Product[(1 - 
      Conjugate[lambda] y^-2) Product[(1 - 
        Conjugate[lambda] y^-2*q^n) (1 - lambda*y^2*q^n), {n, 1, 
      Infinity}], {lambda, {rho, rho^2, rho^4}}]

G[y, q] = 
 y^2*Product[(1 - 
      Conjugate[mu] y^-1) Product[(1 - Conjugate[mu] y^-1*q^n) (1 - 
        mu*y*q^n), {n, 1, Infinity}], {mu, {1, rho^3, rho^5, rho^6}}]

Psi[y, q] = (F[y, q]/G[y, q]) * Product[(1 - q^n)^2, {n, 1, Infinity}]

For some reason, I can compute Series[Psi[y, q], {y, 0, 3}] quite quickly, but the command SeriesCoefficient[Psi[y, q], {y, 0, i}] will not finish for $i=1,2,3$. Why could this be? I've noticed the output of Series[] isn't exactly a power series in y, but rather has some powers of y buried into the functions QPochHammer[] but I don't know how to get them out. Any help is greatly appreciated.

Thanks, Andy.

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