On an extension of generalized incomplete Gamma functions with applications

In this paper we have introduced extensions γ_ν(α, x; b) and Γ_ν(α, x; b) of the generalized Gamma functions γ(α, x; b) and Γ(α, x; b) considered recently by Chaudhry and Zubair. These extensions are found useful in the representations of the Laplace and K-transforms of a class of functions. We have also defined a generalization of the inverse Gaussian distribution. The cumulative and the reliability functions of the generalized inverse Gaussian distribution are expressed in terms of these functions. Some useful properties of the functions are also discussed.