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By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate L\'evy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is…

In this paper, we resurrect a long-forgotten notion of equivalence for univariate polynomials with integral coefficients introduced by Hermite in the 1850s. We show that the Hermite equivalence class of a polynomial has a very natural…

In this paper, we consider the higher-order Changhee numbers and polynomials which are derived from the fermionic p-adic integral on Zp and give some relations between higher-order Changhee polynomials and special polynomials.

Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and…

This paper will be replaced later by a revised version.

Given an n x n matrix over the ring of differential polynomials F(t)[\D;\delta], we show how to compute the Hermite form H of A, and a unimodular matrix U such that UA=H. The algorithm requires a polynomial number of operations in terms of…

We present a new closed form for the interpolating polynomial of the general univariate Hermite interpolation that requires only calculation of polynomial derivatives, instead of derivatives of rational functions. This result is used to…

We introduce a class of doubly indexed real Hermite polynomials and we deal with their related properties like the associated recurrence formulae, Runge's addition formula, generating function and Nielsen's identity.

The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.

We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.

Recently we introduced a new class of relations for Bernoulli symmetric polynomials. This manuscript shows that these relations are valid for arbitrary homogeneous symmetric polynomial. Analysis of these relations leads to the discovery of…

We investigate the symmetric Dunkl-classical orthogonal polynomials by using a new approach applied in connection with the Dunkl operator. The main aim of this technique is to determine the recurrence coefficients first and foremost. We…

The content of this paper is now available as part of arXiv:0802.2019

This results in this paper have been merged with the result in arXiv:1002.3763v1 The authors would like to withdraw this version. Please see arXiv:1008.5356v1 for the merged version.

In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.

We introduce degenerate Hermite polynomials as a degenerate version of the ordinary Hermite polynomials. Then, among other things, by using the formula about representing one lambda-Sheffer polynomial in terms of other lambda-Sheffer…

In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and…

Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.

This semi-expository paper surveys results concerning three classes of orthogonal polynomials: in one non-hermitian variable, in several isometric non-commuting variables, and in several hermitian non-commuting variables. The emphasis is on…

In this paper, we consider the matrix polynomial obtained by using bi-periodic Fibonacci matrix polynomial. Then, we give some properties and binomial transforms of the new matrix polynomials.