Study on r-truncated degenerate stirling numbers of the second kind

TL;DR

This paper introduces and investigates the properties of r-truncated degenerate Stirling numbers of the second kind, extending the classical degenerate Stirling numbers and exploring their explicit formulas and identities.

Contribution

The paper defines r-truncated degenerate Stirling numbers of the second kind and derives their explicit expressions, properties, and identities, expanding the understanding of degenerate special numbers.

Findings

Derived explicit formulas for r-truncated degenerate Stirling numbers.

Established properties and identities relating to these numbers.

Connected the new numbers with other degenerate special numbers and polynomials.

Abstract

The degenerate Stirling numbers of the second kind and of the first kind, which are respectively degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some special numbers and polynomials. The aim of this paper is to consider the r-truncated degenerate Stirling numbers of the second kind, which reduce to the degenerate Stirling numbers of the second for r = 1, and to investigate their explicit expressions, some properties and related identities, in connection with several other degenerate special numbers and polynomials.