A Note About the {Ki(z)} Functions

In the article [Petojevic 2006], A. Petojevi' c verified useful properties of the $K_i(z)$ functions which generalize Kurepa’s [Kurepa 1971] left factorial function. In this note, we present simplified proofs of two of these results and we answer the open question stated in [Petojevic 2006]. Finally, we discuss the differential transcendency of the $K_i(z)$ functions.