Cauchy's theorem

product_(k = 1)^n(1 + y q^k) | = | sum_(m = 0)^n y^m q^(m(m + 1)/2) [n m]_q | = | sum_(m = 0)^n y^m q^(m(m + 1)/2) (q)_n/((q)_m (q)_(n - m)), where [n m]_q is a q-binomial coefficient.

q-binomial coefficient | q-binomial theorem