Some considerations in connection with Kurepa's function

Details Some considerations in connection with Kurepa's function Some considerations in connection with Kurepa's function

2004-06-11

arxiv.org/abs/math/0406235v1

Univ. Beograd. Publ. Elektrotehn. Fak., Ser. Mat. 14 (2003), 30-40

Mathematics

Number Theory

11 pages

Scientific paper

In this paper we consider the functional equation for factorial sum and its particular solutions (Kurepa's function $K(z)$ \cite{Kurepa_71} and function $K_{1}(z)$). We determine an extension of domain of functions $K(z)$ and $K_{1}(z)$ in the sense of Cauchy's principal value at point \cite{Slavic_70}. In this paper we give an addendum to the proof of Slavi\' c's representation of Kurepa's function $K(z)$ \cite{Slavic_73}. Also, we consider some representations of functions $K(z)$ and $K_{1}(z)$ via incomplete gamma function and we consider differential transcendency of previous functions too.

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