Some Q-series Identities Related To Divisor Functions

We give new generalizations of some q-series identities of Dilcher and Prodinger related to divisor functions.The main result can be written as the following:Theorem 1.1. If n≥0,0≤l,m≤n, thenTheorem 1.2. If m≥1,n≥1, thenTheorem 1.3. If m≥0,n≥0, thenSome interesting special cases are also deduced, including an identity related to overpartitions studied by Corteel and Lovejoy.