Multi-Stirling numbers of the second kind
Taekyun Kim, Dae San Kim, Hye Kyung Kim
TL;DR
This paper introduces multi-Stirling numbers of the second kind, generalizing classical combinatorial numbers using the multiple logarithm, and derives several identities involving these and related special numbers.
Contribution
It defines the multi-Stirling numbers of the second kind and establishes new identities connecting them with other multi-numbers based on the multiple logarithm.
Findings
Defined multi-Stirling numbers of the second kind.
Derived identities involving multi-Stirling, multi-Lah, and multi-Bernoulli numbers.
Connected these numbers through properties of the multiple logarithm.
Abstract
The multi-Stirling numbers of the second kind, the unsigned multi-Stirling numbers of the first kind, the multi-Lah numbers and the multi-Bernoulli numbers are all defined with the help of the multiple logarithm, and generalize respectively the Stirling numbers of the second kind, the unsigned Stirling numbers of the first kind, the unsigned Lah numbers and the higher-order Bernoulli numbers . The aim of this paper is to introduce the multi-Stirling numbers of the second kind and to find several identities involving those four numbers defined by means of the multiple logarithm and some other special numbers.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical Inequalities and Applications