Moment Generating Stirling Numbers of the first kind and Applications

Abstract

In this paper we introduce and investigate moment generating Stirling numbers of the first kind, "`MSN1"'. They are inverses of MSN2's, which make the representation of the moments for a lot of statistical distributions in closed formulas possible. Both MSN1's and MSN2's are related to the r-Stirling numbers, and extend their properties to any real third parameter. If the third parameter is a nonnegative integer, r-Stirling numbers can be converted to MSN's and vice versa