[math-fun] Hirschhorn's modular identity

rwg> http://reference.wolfram.com/mathematica/ref/QPochhammer.html (Neat examples) gives "Hirschhorn's modular identity ": [I just pasted the above from my Sent Mail. It ends with ((q;q)_oo)^5=(q^5,q^5)_oo, pasted from the Mma doc, but apparently vaporized on transmission.] rwg> QPochhammer[q, q]^3 = QPochhammer[q^3, q^3] *except* at q^binomial(n,2), n>1. It seems that QPochhammer[q, q]^3 - QPochhammer[q^3, q^3] == -3*Sum[(-1)^n*q^Binomial[n, 2]*Floor[2*n/3], {n, 0, Infinity}] which ought to be some kind of theta derivative, but I can't place it. --rwg