Related papers: Representations of degenerate poly-Bernoulli polyn…

Recently, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with…

In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…

The foremost aim of this study is to introduce and study several combinatorial properties and highlight specific aspects of a new class of polynomials sequences known as degenerate Krawtchouk Appell polynomials associated with the…

Recently, D. S. Kim and T. Kim have studied applications of um- bral calculus associated with p-adic invariant integrals on Zp (see [6]). In this paper, we investigate some interesting properties arising from umbral calculus. These…

By a generalized Delsarte polynomial we mean a Laurent polynomial whose exponent vectors are linearly independent. We consider certain monomial deformations of generalized Delsarte polynomials and study their associated differential…

In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.

In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…

Recently, Komastu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we introduce new generaliza- tion of poly-Cauchy and poly-Bernoulli numbers and polynomials.…

Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic…

In this paper, some formulae for Genoochi polynomials of higher order are derived using the fact that sets of Bernoulli and Euler polynomials of higher order form basis for the polynomial space.

The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…

We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…

Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…

We find solutions for a linear deformation of the symmetric three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is…

Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…

By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their arithmetical and combinatorial properties. As an application, at the end of the…

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…

In this paper, we introduce the Tribonacci and Tribonacci-Lucas quaternion polynomials. We obtain the Binet formulas, generating functions and exponential generating functions of these quaternions. Moreover, we give some properties and…

Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…

In this paper, we introduce two variable degenerate Bell polynomials as a generalization of the degenerate Bell polynomials which were studied earlier. Among other things, we show their connections with Poisson degenerate central moments…