Related papers: $q$-Volkenborn Integration and Its Applications
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
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 derive basic identities of symmetry in two variables related to higher-order q-Euler polynomials and q-analogue of higher order alternating power sums. The derivation of identities are based on the multibvariate p-adic…
The main aim of this paper is to investigate and introduce relations between the numbers of k-ary Lyndon words and unified zeta-type functions which was defined by Ozden et al [15, p. 2785]. Finally, we give some identities on generating…
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.
The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our…
In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all…
We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.
The aim of this paper is to give a novel generalization of the Leibnitz numbers derived from application of the Beta function to the modification for the Bernstein basis functions. We also give some properties of the Leibnitz numbers with…
One familiar with the Euler zeta function, which established the remarkable relationship between the prime and composite numbers, might naturally ponder the results of the application of this special function in cases where there is no…
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.
n this paper, we present $q$-Bernoulli and $q$-Euler polynomials generated by the third Jackson $q$-Bessel function to construct new types of $q$-Lidstone expansion theorem. We prove that the entire function may be expanded in terms of…
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.
By applying an integral representation for $q^{k^{2}}$ we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of $q$-functions and polynomials that…
The main purpose of this paper is to prove an identity of symmetry for the Frobenius-Euler polynomials.
The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less…
In this paper we give new identities involving q-Euler polynomials of higher order.
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
We study a q-logarithm which was introduced by Euler and give some of its properties. This q-logarithm did not get much attention in the recent literature. We derive basic properties, some of which were already given by Euler in a…
Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also…