# New Pentagon Identities Revisited

@article{Jafarzade2018NewPI,
title={New Pentagon Identities Revisited},
journal={Journal of Physics: Conference Series},
year={2018},
volume={1194}
}
• Published 4 December 2018
• Physics, Mathematics
• Journal of Physics: Conference Series
We present a new solution to the pentagon identity in terms of gamma function. We obtain this solution by taking the gamma function limit from the pentagon identity related to the three-dimesional index. This limit corresponds to the identification of the sphere partition function of dual theories and being equivalent to the star-triangle relation in statistical mechanics which corresponds to the “strongly coupled” regime of the Faddeev-Volkov model.
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### D ec 2 02 2 On Bailey pairs for N = 2 supersymmetric gauge theories on S 3 b / Z r

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We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional N = 2 supersymmetric gauge
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: We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional N = 2 supersymmetric gauge

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