The extended hypergeometric class of Lévy

With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo [17]. We give the Wiener–Hopf factorisation of a process in the extended class, and characterise its exponential functional. Fi-nally, we give three concrete examples arising from transformations of stable processes.