Degenerate Lah–Bell polynomials arising from degenerate Sheffer sequences

Abstract

Abstract Umbral calculus is one of the important methods for obtaining the symmetric identities for the degenerate version of special numbers and polynomials. Recently, Kim–Kim (J. Math. Anal. Appl. 493(1):124521, 2021) introduced the λ-Sheffer sequence and the degenerate Sheffer sequence. They defined the λ-linear functionals and λ-differential operators, respectively, instead of the linear functionals and the differential operators of umbral calculus established by Rota. In this paper, the author gives various interesting identities related to the degenerate Lah–Bell polynomials and special polynomials and numbers by using degenerate Sheffer sequences, and at the same time derives the inversion formulas of these identities.

Keywords

• Degenerate Lah–Bell numbers and polynomials
• The degenerate Sheffer sequence
• The degenerate Bernoulli (Euler) polynomials
• The degenerate Frobenius–Euler polynomials
• The degenerate Daehee polynomials
• The degenerate Bell polynomials