Combinatorial identities associated with a bivariate generating function for overpartition pairs

We obtain a three-parameter q -series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new combinatorial significance in connection with N ( r , s m n ) function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy Osburn. For example, one identities gives closed-form evaluation double series terms Chebyshev polynomials the second kind, thereby resulting an analogue Euler's pentagonal number theorem. Other applications include expressing multi-sum involving partition p relating to weight 7/2 theta series.