Related papers: On the Euler Numbers and its Applications

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

Recently, the higher-order q-Euler polynomials and multiple q-Euler zeta functions are introduced by T. Kim ([8, 9]). In this paper, we investigate some symmetric properties of the multiple q-Euler zeta function and derive various…

In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.

In this paper we consider the Witt's fprmula related to Carlitz's type q-Euler numbers and polynomials.

In this paper, we give the determinant expressions of the hypergeometric Bernoulli numbers, and some relations between the hypergeometric and the classical Bernoulli numbers which include Kummer's congruences. By applying Trudi's formula,…

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally,…

We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of…

In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…

In this paper we will investigate properties of modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measures.

We describe applications of the classical umbral calculus to bilinear generating functions for polynomial sequences, identities for Bernoulli and related numbers, and Kummer congruences.

In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.

We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.

In this note we prove combinatorially some new formulas connecting poly-Bernoulli numbers with negative indices to Eulerian numbers.

In this paper we define the generalized q-analogues of Euler sums and present a new family of identities for q-analogues of Euler sums by using the method of Jackson q-integral rep- resentations of series. We then apply it to obtain a…

In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the…

This note highlights an interesting connection between Euler sums of even weight and prime 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.

In the paper, 2 explicit formulas for the Euler numbers of the second kind are obtained. Based on those formulas a exponential generating function is deduced. Using the generating function some well-known and new identities for the Euler…

In this paper, by using some families of special numbers and polynomials with their generating functions, we give various properties of these numbers and polynomials. These numbers are related to the well-known numbers and polynomials,…