Explicit identities for Lévy processes associated to symmetric stable processes

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In this paper we introduce a new class of Lévy processes which we call hypergeometric-stable Lévy processes, because they are obtained from symmetric stable processes through several transformations and where the Gauss hypergeometric function plays an essential role. We characterize the Lévy measure of this class and obtain several useful properties such as the Wiener Hopf factorization, the characteristic exponent and some associated exit problems.