A set of new three-parameter entropies in terms of a generalized incomplete Gamma function

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 S d , c 1 , c 2 [ p ] ∝ ∑ i Γ ( d + 1 , 1 − c 1 ln p i , 1 − c 2 ln p i ) . 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.