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 _Sd,c1,c2[p]∝_∑iΓ(d+1,1−_c1ln_pi,1−_c2ln_pi)$S_{d,c_1,c_2}\left[p\right]\propto {\sum }_i\Gamma (d+1,1-c_{1}ln{p}_i,1-c_{2}ln{p}_i)$. 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.