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A bstract We detail the properties of the Veneziano, Virasoro, and Coon amplitudes. These tree-level four-point scattering amplitudes may be written as infinite products with an infinite sequence of simple poles. Our approach for the Coon amplitude uses the mathematical theory of q -analysis. We interpret the Coon amplitude as a q -deformation of the Veneziano amplitude for all q ≥ 0 and discover a new transcendental structure in its low-energy expansion. We show that there is no analogous q -deformation of the Virasoro amplitude.
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Geiser et al. (2022) studied this question.
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