Korobov polynomials of the third kind and of the fourth kind

The first degenerate version of the Bernoulli polynomials of the second kind appeared in the paper by Korobov (Math Notes 2:77-19, 1996; Proceedings of the IV international conference modern problems of number theory and its applications, pp 40-49, 2001). In this paper, we study two degenerate versions of the Bernoulli polynomials of the second kind which will be called Korobov polynomials of third kind and of the fourth kind. Some properties, identities, recurrence relations and connections with other polynomials are investigated by using umbral calculus.