Moment Generating Stirling Numbers of the first kind and Applications

Name: Moment Generating Stirling Numbers of the first kind and Applications
Creator: Frank, Ludwig
Keywords: 11B73, 05A19, 05A10, 60C05, FOS: Mathematics, Mathematics - Combinatorics, G.2.1, Combinatorics (math.CO)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2023Embargo end date: 01 Jan 2023Publisher:arXiv

Authors: Frank, Ludwig;

doi: 10.48550/arxiv.2310.12607

arXiv: http://arxiv.org/abs/2310.12607

Moment Generating Stirling Numbers of the first kind and Applications

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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.

Keywords

11B73, 05A19, 05A10, 60C05, FOS: Mathematics, Mathematics - Combinatorics, G.2.1, Combinatorics (math.CO)

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