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An historical prolegomenon to the occurrence of the resonance dual models: the Watson-Sommerfeld transform

We would like to discuss, within the inherent historical context, upon one of the main works of fundamental physics which has led to the formulation of the early resonance dual models prior to string theory. In fact, we shall focus on certain aspects of the fundamental Tullio Regge work of 1959, to be precise, on certain mathematical methods handled by him to pursue his original intentions mainly motivated to prove some double dispersion relations into the framework of non-relativistic potential scattering.