Construction of partially degenerate Bell–Bernoulli polynomials of the first kind and their certain properties

Abstract Various applications of degenerate polynomials in different areas call for the thoughtful study and research, and many extensions and variants can be found in the literature. In this paper, we introduce partially degenerate Bell–Bernoulli polynomials of the first kind and investigate their properties and identities. Furthermore, we introduce a generalized form of partially degenerate Bell–Bernoulli polynomials of the first kind and derive some interesting properties and identities. The results obtained are of general character and can be reduced to yield formulae and identities for relatively simple polynomials and numbers.