Related papers: Probabilistic degenerate poly-Bell polynomials ass…
Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and…
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.
The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two…
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…
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…
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…
In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.
Degenerate Dowling and degenerate r-Dowling polynomials were introduced earlier as degenerate versions and further generalizations of Dowling and r-Dowling polynomials. The aim of this paper is to show their connections with Poisson…
In this paper, we introduce the degenerate zero-truncated Poisson random variables whose probability mass functions are a natural extension of the zero-truncated Poisson distributions, and investigate various properties of those random…
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Assume that the moment generating function of the random vari able Y exists in a neighborhood of the origin. We introduce the probabilistic multi-Stirling numbers of the second kind associated with Y and the proba bilistic multi-Lah numbers…
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. Recently, probabilistic Stirling numbers of the first kind and of the second kind associated with Y have been introduced. However,…
In recent years, studying degenerate versions of various special polynomials and numbers have attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials and…
In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce…
In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials…
This paper is concerned with multivariate refinements of the gamma-positivity of Eulerian polynomials by using the succession and fixed point statistics. Properties of the enumerative polynomials for permutations, signed permutations and…
We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present…