Rahman’s Biorthogonal Rational Functions and Superconformal Indices

Journal article, 2018

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 10 W 9 -functions or their degenerate cases. We also give new bilateral extensions of the Jackson and q-Saalschütz summation formulas and new continuous and discrete biorthogonality measures for Rahman’s functions.