$\lambda$-analogues of r-Stirling numbers of the first kind

TL;DR

This paper introduces and explores $5$-analogues of r-Stirling numbers of the first kind, establishing their recurrence relations and connections with existing combinatorial numbers and polynomials.

Contribution

It provides new recurrence relations and links these $5$-analogues to $5$-Stirling numbers and higher-order Daehee polynomials, expanding the combinatorial framework.

Findings

Derived recurrence relations for $5$-analogues

Established connections with $5$-Stirling numbers

Linked to higher-order Daehee polynomials

Abstract

In this paper, we study $\lambda$-analogues of the r-Stirling numbers of the first kind which have close connections with the r-Stirling numbers of the first kind and $\lambda$-Stirling numbers of the first kind. Specifically, we give the recurrence relations for these numbers and show their connections with the $\lambda$-Stirling numbers of the first kind and higher-order Daehee polynomials.