Study of degenerate derangement polynomials by λ-umbral calculus - Yun Sang Jo; Park Jin-Woo (Demonstratio Mathematica, 2023)
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 λλ -Sheffer sequences and λλ -umbral calculus, which are defined by Kim-Kim (Degenerate Sheffer sequences and λλ -Sheffer sequences, J. Math. Anal. Appl. 493 (2021), 124521, 21pp).