Dixit, AtulAtulDixitGoswami, AnkushAnkushGoswami2025-08-282025-08-282022-01-01https://arxiv.org/abs/2201.06746https://d8.irins.org/handle/IITG2025/20101We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler's pentagonal number theorem. Another of our results expresses a multi-sum involving N(r,s,m,n) in terms of just the partition function p(n). Using a result of Shimura we also relate a certain double series with a weight 7/2 theta series.en-USCombinatorial identitiesCombinatoricsNumber TheoryPartition functionChebyshev polynomialse-Printe-Print123456789/555