相关论文: A note on q-Euler numbers and polynomials
We give some new identities for (h; q)-Genocchi numbers and polynomials by means of the fermionic p-adic q-integral on Zp and the weighted q-Bernstein polynomials.
In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Theory of Analytic…
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…
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.
The main objective of this paper is to introduce the modified q-Genocchi polynomials and to define their generating function. In the paper, we show new relations, which are explicit formula, derivative formula, multiplication formula, and…
In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
The Cauchy polynomials with a $q$ parameter were recently defined, and several arithmetical properties were studied. In this paper, we establish explicit formulae for computing the Cauchy polynomials with a $q$ parameter in terms of…
In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…
We present a method for the solution of polynomial equations. We do not intend to present one more method among several others, because today there are many excellent methods. Our main aim is educational. Here we attempt to present a method…
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 paper, we give some interesting and new identities of q-Bernoulli numbers which are derived from convolutions on the ring of p-adic integers.
The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…
In this paper we prove that q-Euler numbers are occured in the coefficients of some stirling type seies for p-adic analytic q-log gamma function
In this paper, the authors deal with the $q$-Genocchi numbers and polynomials with weight zero. They discover some interesting relations via the $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and familiar basis Bernstein polynomials. Finally,…
By applying the p-adic q-Volkenborn Integrals including the bosonic and the fermionic p-adic integrals on p-adic integers, we define generating functions, attached to the Dirichlet character, for the generalized Apostol-Bernoulli numbers…
This paper aims to construct a new family of numbers and polynomials which are related to the Bell numbers and polynomials by means of the confluent hypergeometric function. We give various properties of these numbers and polynomials…
In this article, the 2-iterated q-Appell family is introduced. Certain 2-iterated q-Appell and mixed type q-special polynomials are considered as members of this family. The numbers related to these polynomials are obtained. The determinant…
Given a zero-dimensional ideal I in a polynomial ring, many computations start by finding univariate polynomials in I. Searching for a univariate polynomial in I is a particular case of considering the minimal polynomial of an element in…