2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131460In 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.Accepted in Rocky Mountain Journal of mathematicsNumber TheoryComplex Variablestext