Related papers: On poly-Bell numbers and polynomials
New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a composita and a Bell polynomial is demonstrated. Main…
The aim of this paper is to give some combinatorial relations linked polynomials generalizing those of Appell type to the partial r-Bell polynomials. We give an inverse relation, recurrence relations involving some family of polynomials and…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinite Euler-type products. By analyzing the logarithmic…
The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are…
The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials.…
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate…
In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable Y, arising from the…
In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfying moment conditions, we use the generating function of these…
Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…
The aim of this study is to show that harmonic geometric polynomials can be represented in terms of geometric polynomials. This problem was first considered by Keller [14]; however, the corresponding coefficients were not fully determined.…
The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include…
We introduce and study a `level two' generalization of the poly-Bernoulli numbers, which may also be regarded as a generalization of the cosecant numbers. We prove a recurrence relation, two exact formulas, and a duality relation for…
The aim of this paper is to introduce truncated degenerate Bell polynomials and numbers and to investigate some of their properties. In more detail, we obtain explicit expressions, identities involving other special polynomials, integral…
We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is…
We introduce poly-Cauchy permutations that are enumerated by the poly-Cauchy numbers. We provide combinatorial proofs for several identities involving poly-Cauchy numbers and some of their generalizations. The aim of this work is to…
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…