Degenerate Stirling Polynomials of the Second Kind and Some Applications

Abstract

Recently, the degenerate $\lambda$ -Stirling polynomials of the second kind were introduced and investigated for their properties and relations. In this paper, we continue to study the degenerate $\lambda$ -Stirling polynomials as well as the r-truncated degenerate $\lambda$ -Stirling polynomials of the second kind which are derived from generating functions and Newton’s formula. We derive recurrence relations and various expressions for them. Regarding applications, we show that both the degenerate $\lambda$ -Stirling polynomials of the second and the r-truncated degenerate $\lambda$ -Stirling polynomials of the second kind appear in the expressions of the probability distributions of appropriate random variables.