Abstract Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A ′ n +1 ( x ) = + 1) with 0 constant polynomial. This allows us to obtain in simple way some known relations involving Apostol-Bernoulli polynomials, Apostol-Euler and generalized Bernoulli attached primitive Dirichlet character.

We develop polynomials in z ∈ C for which some generalized harmonic numbers are special cases at z= 0. By using the Riordan array method, we explore interesting relationships between these polynomials, the generalized Stirling polynomials, the Bernoulli polynomials, the Cauchy polynomials and the Nörlund polynomials. © 2007 Elsevier B.V. All rights reserved.

In this paper, we give some further properties of p-adic q-L-function of two variables, which is recently constructed by Kim 2005 and Cenkci 2006 . One of the applications of these properties yields general classes of congruences for generalized q-Bernoulli polynomials, which are qextensions of the classes for generalized Bernoulli numbers and polynomials given by Fox 2000 , Gunaratne 1995 , an...

By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §

Recently, several Bell based polynomials such as Bernoulli, Euler, Genocchi and Apostol versions were defined investigated. The main aim of this paper is to introduce the general family Appell polynomials, which includes many new members in addition existing ones, investigate their properties including determinantal representation, recurrence relation, derivative formula, shift operators differ...

We introduce and investigate the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials by means of a suitable theirs generating polynomials. We establish several interesting properties of these polynomials. Also, we gave some propositions two theorems and one corollary.

and Applied Analysis 3 see 3, 4, 15, 16 . By 1.5 and 1.7 , the Witt’s formula for the q-Bernoulli numbers with weight α is given by ∫ Zp x qαdμq x β̃ α n,q , where n ∈ Z . 1.8 The q-Bernoulli polynomials with weight α are also defined by

The generalized mixed type Bernoulli-Gegenbauer polynomials of order α >−1/2 are special obtained by use the generating function method. These represent an interesting mixture between two classes functions, namely Bernoulli and Gegenbauer polynomials. main purpose this paper is to discuss some their algebraic analytic properties.

is a well-known formula from classical analysis giving a relation between the finite sum of values of a function f , whose first m derivatives are absolutely integrable on [a, n], and its integral, for a,m, n ∈ N, a < n. This elementary formula appears often in introductory texts [2, 17], usually in reference to a particular application—Stirling’s asymptotic formula. However, general approaches...