Identities for degenerate Bernoulli polynomials and Korobov polynomials of the first kind

Abstract

In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous results, to degenerate Bernoulli polynomials and Korobov polynomials of the first kind and get some new identities. In addition, letting $\lambda~\rightarrow~0$ in such identities gives usthose for Bernoulli polynomials and Bernoulli polynomials of the second kind.