In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.

Recently, several Bell based polynomials such as Bernoulli, Euler, Genocchi and Apostol versions were defined investigated. The main aim of this paper is to introduce the general family Appell polynomials, which includes many new members in addition existing ones, investigate their properties including determinantal representation, recurrence relation, derivative formula, shift operators differ...

In this paper, we introduce a new type degenerate Stirling numbers of the second kind and their Bell polynomials, which is different from studied so far. We investigate explicit formula, recurrence relation Dobinski-like formula kind. also derived several interesting expressions identities for bell polynomials these including generating function, relation, differential equation with Bernoulli n...

We survey a family of polynomials that are very useful in all kinds power series manipulations, and appearing more frequently the literature. Applications to formal series, generating functions asymptotic expansions described, we discuss related work De Moivre, Arbogast Bell.

In this note, we first derive an exponential generating function of the alternating run polynomials. We then deduce explicit formula polynomials in terms partial Bell

In the paper, the author introduces the notions “multi-order logarithmic numbers” and “multi-order logarithmic polynomials”, establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faà di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal...

Abstract In this paper, we study degenerate complete and partial Bell polynomials establish some new identities for those polynomials. addition, investigate the connections between modified polynomials, which are closely related to joint distribution of weighted sums independent Poisson random variables.