Abstract
In this paper, by considering the first three Khinchin axioms (K1–K3) and neglecting the fourth (K4), a set of new three-parameter entropies will be introduced which are expressed in terms of a generalized incomplete Gamma function as Sd,c1,c2[p]∝∑iΓ(d+1,1−c1lnpi,1−c2lnpi). Also, its asymptotic behavior will be found and it will be shown that, for some special values of parameters, some known entropies like Tsallis, Kaniadakis and Abe entropies are recovered.
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