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

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