in http://gosper.org/fst.pdf, namely ((-1 + QPochhammer[a, p])*QPochhammer[q, q])/a == Sum[(q^((1/2)*n*(1 + n))* Product[1 - a*p^k + c*p^k*q^k - q^(k - n), {k, 0, Infinity}])/ ((-1)^n*((a - c*q^n)*QPochhammer[q, q, n])), {n, 0, Infinity}] eluded our attempts to rederive it, despite the hints near the end of the paper. Those led me instead to ((-1 + QPochhammer[a, p])*QPochhammer[q, q])/a == Sum[-(((-1)^n*q^((1/2)*n*(3 + n))* Product[1 + (-1 + a*p^k)*q^(k - n) + (a*c*p^k)/q^n, {k, 0, Infinity}])/(a*(c + q^n)* QPochhammer[q, q, n])), {n, 0, Infinity}] Series sez they both work! The summands are utterly unlike, even for n = 0. (Idiot Mma takes ~minutes to plug n=0 into the ratio of the summands! No sums, just products.) Changing c->-a/c in the former, even though unmentioned in the paper, ((-1 + QPochhammer[a, p])*QPochhammer[q, q])/a == Sum[((-1)^n*c*q^((1/2)*n*(3 + n))* Product[1 + (-1 + a*p^k)*q^(k - n) - (a^2*p^k)/(q^n*c), {k, 0, Infinity}])/(a*(a - c*q^n)* QPochhammer[q, q, n]), {n, 0, Infinity}] did zilch to reconcile the summands. So, I don't know where the bleep (4) came from, but I've regained some facility with nonlocal derangement, and now we have (4a) and (4b). --rwg