Some q-series identities related to divisor functions Original Research Article

The generating functions of the divisor functions σk(n) = Σd|ndk are expressed as sums of products of the series Um(q):=∑n=1∞nmqn∏j=n+1∞(1−qj), m=1,…,k+1, and vice versa. Other related q-series identities are derived, including ∑n=k∞nk(1−qj=∑j1=1∞qj11−qj1 ∑j2=1j1qj21−qj2… ∑jk=1jk−1qjk1−qjk.