Related papers: q-analogue of Euler-Barnes' numbers and polynomial…

We give a q-analogue of Gauss' divisibility theorem

In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

In this paper we construct a new q-Euler numbers and polynomials. By using these numbers and polynomials, we give the interesting formulae related to alternating sums of powers of consecutive q-integers following an idea due to Euler.

In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.

In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.

We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.

We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.

Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.

In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.

In this paper, we consider the new q-extension of Frobenius-Euler numbers and polynomials and we derive some interesting identities from the orthogonality type properties for the new q-extension of Frobenius-Euler polynomials. Finally we…

In this paper we investigate some interesting of the (h,q)-extension of Euler numbers and polynomials. Finally, we will give some relations between these numbers anf polynomials

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the…

In this paper we consider the extended q-Bernstein polynomials which are constructed by T. Kim and we investigate some properties.

In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.

The purpose of this paper is to investigate some properties of q-Euler numbers and polynomials with weight 0. From those q-Euler numbers with weight 0, we derive some identities on the q-Euler numbers and polynomials with weight 0.

This article considers some q-analogues of classical results concerning the Ehrhart polynomials of Gorenstein polytopes, namely properties of their q-Ehrhart polynomial with respect to a good linear form. Another theme is a specific linear…

In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.

The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition…

In this note we show that various natural q-analogues of the Catalan numbers can be obtained in a uniform way. Furthermore we compute their Hankel determinants.