Poly-frobenius-genocchi polynomials: A probabilistic perspective with applications

Abstract

In the paper, we introduce probabilistic extensions of poly-Frobenius-Genocchi polynomials and modified probabilistic Genocchi-polynomials. By making use of their generating functions, we derive explicit identities and a symmetric relation. In special cases, the obtained results reduce to classical one. Additionally, by choosing appropriate random variable, we obtain new identities including Stirling numbers of the first kind, Frobenius-Euler numbers, Frobenius-Genocchi numbers and Bernoulli numbers of negative order. © 2025 NSP