In this paper, authors found a new and interesting identity between Changhee polynomials and some degenerate polynomials such as degenerate Bernoulli polynomials of the first and second kind, degenerate Euler polynomials, degenerate Daehee polynomials, degenerate Bell polynomials, degenerate Lah–Bell polynomials, and degenerate Frobenius–Euler polynomials and Mittag–Leffer polynomials by using λ -Sheffer sequences and λ -differential operators to find the coefficient polynomial when expressing the n -th Changhee polynomials as a linear combination of those degenerate polynomials. In addition, authors derive the inversion formulas of these identities.

In this article, we derived various identities between the degenerate poly-Daehee polynomials and some special polynomials by using λ -umbral calculus by finding the coefficients when expressing degenerate poly-Daehee polynomials as a linear combination of degenerate Bernoulli polynomials, degenerate Euler polynomials, degenerate Bernoulli polynomials of the second kind, degenerate Daehee polynomials, Changhee polynomials, degenerate Bell polynomials, and degenerate Lah-Bell polynomials.

In the 1970s, Gian-Carlo Rota constructed the umbral calculus for investigating the properties of special functions, and by Kim-Kim, umbral calculus is generalized called λ -umbral calculus. In this paper, we find some important relationships between degenerate Changhee polynomials and some important special polynomials by expressing the Changhee polynomial as a linear combination of some special polynomials. In addition, we derive some interesting identities related to degenerate poly-Changhee polynomials and some important special functions by using λ -umbral calculus.