Rahman's biorthogonal functions and superconformal indices

Preprint, 2016

We study biorthogonal functions related to basic hypergeometric integrals with coupled continuous and discrete components. Such integrals appear as superconformal indices for three-dimensional quantum field theories and also in the context of solvable lattice models. We obtain explicit biorthogonal systems given by products of two of Rahman's biorthogonal rational 10W9-functions or their degenerate cases. We also give new bilateral extensions of the Jackson and q-Saalschutz summation formulas and new continuous and discrete biorthogonality measures for Rahman's functions.