Some identities involving degenerate r-Stirling numbers

TL;DR

This paper derives new mathematical identities involving degenerate r-Stirling numbers of both kinds using inverse relations, expanding understanding of these special combinatorial numbers.

Contribution

It introduces novel identities for degenerate r-Stirling numbers of the first and second kinds based on inverse relations, enhancing their theoretical framework.

Findings

Derived identities for degenerate r-Stirling numbers

Extended the theoretical understanding of these special numbers

Provided formulas that could facilitate further research

Abstract

Recently, authors studied the unsigned degenerate r-Stirling number of the first kind and the degenerate r-Stirling number of the second kind, respectively of which are the degenerate versions of the unsigned r-Stirling numbers of the first kind and those of the r-Stirling numbers of the second kind. The aim of this paper is to derive some identities involving such special numbers from the inverse relations for them.