Some considerations in connection with alternating Kurepa's function

Abstract

In this paper, we consider the functional equation for alternating factorial sum and some of its particular solutions alternating Kurepa's function A(z) and function A 1(z). We determine an extension of domain of functions A(z) and A 1(z) in the sense of the principal value at point. We give a new representation of alternating Kurepa's function A(z), which is an analogue of Slavić’s representation of Kurepa's function K(z). Also, we consider some representations of functions A(z) and A 1(z) via incomplete gamma function, and we consider differential transcendency of previous functions too.