Related papers: Certain study of generalized Apostol-Bernoulli pol…
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.
In this paper, we derive new matrix representation for Daehee numbers and polynomials, the lambda-Daehee numbers and polynomials and the twisted Daehee numbers and polynomials. This helps us to obtain simple and short proofs of many…
The aim of this paper is to further study some properties and identities on the degenerate Fubini and the degenerate Bell polynomials which are degenerate versions of the Fubini and the Bell polynomials, respectively. Especially, we find…
Inspired by the framework of operational methods and based on the generating functions of Legendre-Gould Hopper polynomials and Sheffer sequences, we discuss certain new mixed type polynomials and their important properties. We show that…
In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these…
We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the…
In this paper, we introduce the degenerate multiple polyexponential functions which are multiple versions of the degenerate modified polyexponential functions. Then we consider the degenerate multi-poly-Genocchi polynomials which are…
The main contribution of this paper is to find a representation of the class $\mathcal{F}_d(p)$ of multivariate Bernoulli distributions with the same mean $p$ that allows us to find its generators analytically in any dimension. We map…
In this article, we introduce the simplicial $d$-polytopic numbers defined on generalized Fibonacci polynomials. We establish basic identities and find $q$-identities known. Furthermore, we find generating functions for the simplicial…
In this paper, we study some properties of Changhee's q-Bernou lli polynomials which are derived from p-adic invariant integral on Zp. By using these properties, we give some interesting identities related to higher- order q-Bernoulli…
In this paper, we establish some formulas for the noncentral Tanny-Dowling polynomials including sums of products and explicit formulas which are shown to be generalizations of known identities. Other important results and consequences are…
We investigate the representation of arbitrary polynomials using probabilistic Bernoulli and degenerate Bernoulli polynomials associated with a random variable $Y$, whose moment generating function exists in a neighborhood of the origin. In…
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral…
It is demonstrated how an explicit expression of the (partial) sum of Tetranacci numbers can be found and proved using generating functions and the Hadamard product. We also provide a Binet-type formula for generalized Fibonacci numbers, by…
The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers. The present paper deals with weighted q-Bernstein polynomials and q-Genocchi numbers…
In this work we derive a bilateral generating function involving the product of an Appell-type product of the Bernoulli and Euler polynomials over independent indices and orders. This function is expressed in terms of the Hurwitz zeta…
We present a formula for a generalisation of the Eulerian polynomial, namely the generating polynomial of the joint distribution of major index and descent statistic over the set of signed multiset permutations. It has a description in…
In this paper, by using the orthogonality type as defined in the umbral calculus, we derive explicit formula for several well known polynomials as a linear combination of the Apostol-Euler polynomials.