Study of degenerate derangement polynomials by λ-umbral calculus

Abstract

Abstract In the 1970s, Rota began to build completely rigid foundations for the theory of umbral calculus based on relatively modern ideas of linear functions and linear operators. Since then, umbral calculus has been used in the study of special functions in various fields. In this article, we derive some new and interesting identities related to degenerate derangement polynomials and some special polynomials by using λ \lambda -Sheffer sequences and λ \lambda -umbral calculus, which are defined by Kim-Kim (Degenerate Sheffer sequences and λ \lambda -Sheffer sequences, J. Math. Anal. Appl. 493 (2021), 124521, 21pp).