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Rahman’s Biorthogonal Rational Functions and Superconformal Indices

Journal article
Authors Hjalmar Rosengren
Published in Constructive Approximation
Volume 47
Pages 529-552
ISSN 0176-4276
Publication year 2018
Published at Department of Mathematical Sciences, Analysis and Probability Theory
Pages 529-552
Language en
Keywords Basic hypergeometric integral, Basic hypergeometric series, Biorthogonal rational function, Superconformal index
Subject categories Mathematical Analysis, Computational Mathematics, Algebra and Logic


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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