Related papers: Dunkl-Gamma Type Operators including Appell Polyno…
In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on…
Suppose that $\Gamma$ is a continuous and self-adjoint Hankel operator on $L^2(0, \infty)$ and that $Lf=-(d/dx(a(x)df/dx))+b(x)f(x)$ with $a(0)=0$. If $a$ and $b$ are both quadratic, hyperbolic or trigonometric functions, and $\phi$…
We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually multipliers in the abelian group of the Appell polynomials endowed with the operation…
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…
In this paper, we construct a Durrmeyer-type variant of Gr\"unwald interpolation operators on the space $L^p[0,{\pi}]$. We prove their fundamental properties, including boundedness and convergence in the $L^p$-norm. We establish the…
We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies…
In this paper we calculate some Generalized Selberg integrals. The answer is expressed in terms of $\Gamma$-functions. Integrals of this type serve as normalization constants or directly via undoing 2-D integrals for determination of…
The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We…
We study the Hp-Lq boundedness of certain integral operators of fractional type.
A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lam\'e operator.
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
Some weighted inequalities for the maximal operator with respect to the discrete diffusion semigroups associated with exceptional Jacobi and Dunkl-Jacobi polynomials are given. This setup allows to extend the corresponding results obtained…
In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of…
An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the…
In this paper, we investigate some properties of q-Bernoulli polynomi- als arising from q-umbral calculus. Finally, we derive some interesting identities of q-Bernoulli polynomials from our investigation.
In this paper we characterize local exponential monomials and polynomials on different types of Abelian groups and we prove Montel-type theorems for these function classes.
This article contributes to the new summation of Sz\'asz operators with the help of Appell polynomials of class $A^{2}$. We verified Bohman-Korovkin's theorem and prove the convergence results like Lipschitz-type space, Voronvaskaja-type…
Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…