product_(k=1)^∞ (1 - z^(2 k)) (1 - z^(2 k - 1) w^2) (1 + z^(2 k - 1)/w^2) = sum_(k=-∞)^∞ z^(k^2) w^(2 k) ( product_(i=1)^∞(1 + z^(2 i))) ( product_(j=1)^∞(1 + z^(2 j - 1))) product_(k=1)^∞(1 - z^(2 k - 1)) = 1