We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic proofs and physical interpretations of the presented identities.
Gahramanov, I., & Rosengren, H. (2016). Basic hypergeometry of supersymmetric dualities. Nuclear Physics B, 913, 747–768. https://doi.org/10.1016/j.nuclphysb.2016.10.004