A note on degenerate r-Stirling numbers

Abstract

Abstract The aim of this paper is to study the unsigned degenerate r-Stirling numbers of the first kind as degenerate versions of the r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind as those of the r-Stirling numbers of the second kind. For the degenerate r-Stirling numbers of both kinds, we derive recurrence relations, generating functions, explicit expressions, and some identities involving them.

Keywords

• Unsigned degenerate r-Stirling numbers of the first kind
• Degenerate r-Stirling numbers of first kind
• Degenerate r-Stirling numbers of second kind