On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms

In this paper we introduce decomposition functions CΓ(α,x;ω), SΓ(α,x;ω), Cγ(α,x;ω) and Sγ(α,x;ω) of the generalized gamma functions. These functions are found useful in the analytic study of the temperature distribution of a semi-infinite solid with periodic boundary conditions and to the theory of Fourier transforms. Several new identities involving the Fourier transforms are investigated and some of the classical ones are recovered as special cases. For numerical and scientific computations, tabular and graphical representations of the functions CΓ(α,x;ω) and SΓ(α,x;ω) are also given.