A solution to Open Problem 3.137 by O. Furdui on multiple factorial series

TL;DR

This paper provides a closed-form solution for a multiple factorial series, addressing an open problem by O. Furdui, using properties of divided differences, and extends to similar series and generalizations.

Contribution

It introduces a novel closed-form expression for a specific multiple factorial series, solving an open problem and applying divided differences to broader series.

Findings

Closed-form expression for the multiple factorial series

Solution to Open Problem 3.137 by O. Furdui

Method applicable to similar series and generalizations

Abstract

In this paper we give a closed expression for a multiple factorial series, solving Open Problem 3.137 in a recent book by O. Furdui. The method is based on properties of divided differences. It applies also to similar series and certain generalizations.