Related papers: A unified matrix approach to the representation of…
Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a…
Motivated by the effective impact of the Pascal functional and the Wronskian matrices, we investigate several identities and differential equation for the Sheffer-Appell polynomial sequence by using matrix algebra. The matrix approach,…
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…
In this paper, certain mixed special polynomial families associated with Appell sequences are introduced and their properties are established. Further, operational rules providing connections between these families and the known special…
This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the…
In this paper, by the umbral calculus method, we give a remarkable congruence involving Appell polynomials. Some applications on derangement polynomials are also presented.
The Pascal matrix, which is related to Pascal's triangle, appears in many places in the theory of uniform distribution and in many other areas of mathematics. Examples are the construction of low-discrepancy sequences as well as normal…
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
The main purpose of this paper is to study generalized (self-) reciprocal Appell polynomials, which play a certain role in connection with Faulhaber-type polynomials. More precisely, we show for any Appell sequence when satisfying a…
This research is aimed to give a determinantal definition for the $q$-Appell polynomials and show some classical properties as well as find some interesting properties of the mentioned polynomials in the light of the new definition.
We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples. In…
In this paper we aim to specify some characteristics of the so called family of $q$-Appell Polynomials by using $q$-Umbral calculus. Next in our study, we focus on $q$-Genocchi numbers and polynomials as a famous member of this family. To…
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of…
The aim of the present paper is to introduce Dunkl-Gamma type operators in terms of Appell polynomials and to investigate approximating properties of these operators.
The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formullae for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
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 outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…