Related papers: On a class of polynomials connected to Bell polyno…

The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…

We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including…

In this article we point out interesting connections among Lah numbers, Laguerre polynomials of order negative one, and exponential polynomials. We also discuss several different expressions for the higher order derivatives of exp (1/x). A…

Partial ordinary Bell polynomials are used to formulate and prove a version of the Fa\`{a} di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two…

In this paper, we study the degenerate central complete and incomplete Bell polynomials which are degenerate versions of the recently introduced central complete and incomplete Bell polynomials and also central analogues for the degenerate…

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.

In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev…

In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell…

In this paper, we take advantage of the Mellin type derivative to produce some new families of polynomials whose coefficients involve r-Lah numbers. One of these polynomials leads to rediscover many of the identities of r-Lah numbers. We…

We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a…

In this paper, we study linear differential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.

In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number--theoretical properties. A new class of…

In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated…

In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the…

In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.