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arXiv · 1612.05051

Rahman's biorthogonal functions and superconformal indices

Hjalmar Rosengren
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Abstract

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.

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Hjalmar Rosengren. 2016-12-15. Rahman's biorthogonal functions and superconformal indices. https://arxiv.org/abs/1612.05051

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