Some considerations in connection with alternating Kurepa's function
Abstract
Description
In this paper we consider the functional equation for alternating factorial sum and some of its particular solutions (alternating Kurepa's function $A(z)$ from [Petojevic_02] 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 [Slavic_73], [Mijajlovic & Malesevic_07]. Using the methods from [Slavic_73] and [Malesevic_03] we give a new representation of alternating Kurepa's function $A(z)$, which is an analog of Slavi\' c's representation of Kurepa's function $K(z)$ [Slavic_73], [Marichev_83]. 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.