Some inequalities for Kurepa's function

TL;DR

This paper explores inequalities and recurrence relations for Kurepa's function, providing new bounds and functional relations that enhance understanding of its properties for positive arguments.

Contribution

It introduces new recurrence relations and inequalities for Kurepa's function, expanding the analytical tools available for its study.

Findings

Derived new recurrence relations for Kurepa's function.

Established inequalities bounding Kurepa's function for positive x.

Enhanced understanding of Kurepa's function's behavior for positive arguments.

Abstract

In this paper we consider Kurepa's function $K(z)$ \cite{Kurepa_71}. We give some recurrent relations for Kurepa's function via appropriate sequences of rational functions and gamma function. Also, we give some inequalities for Kurepa's function $K(x)$ for positive values of $x$.