λ-Analogues of Stirling polynomials of the first kind and their applications

Abstract

Abstract Recently, λ-analogues of Stirling numbers of the first kind were studied. In this paper, we introduce, as natural extensions of these numbers, λ-Stirling polynomials of the first kind and r-truncated λ-Stirling polynomials of the first kind. We give recurrence relations, explicit expressions, some identities, and connections with other special polynomials for those polynomials. Further, as applications, we show that both of them appear in an expression of the probability mass function of a suitable discrete random variable, constructed from λ-logarithmic and negative λ-binomial distributions.

Keywords

• λ-Stirling polynomials of the first kind
• r-truncated λ-Stirling polynomials of the first kind
• r-truncated λ-logarithmic distribution
• Negative λ-binomial distribution