q-Apostol–Euler Polynomials and q-Alternating Sums

Basic properties are established and generating functions are obtained for the q -Apostol–Euler polynomials. We define q -alternating sums and obtain q -extensions of some formulas from Integral Transform. Spectr. Funct., 20, 377–391 (2009). We also deduce an explicit relationship between the q -Apostol–Euler polynomials and the q -Hurwitz–Lerch zeta-function.Встановлено основні властивості та твірні функції q-полiномiв Апостола-Ейлера. Визначено q-знакозмінні суми та отримано q-продовження деяких формул з [Integral Transform. Spec. Funct.-2009.-20.-P. 377-391]. Виведено також явне співвідношення між q-поліномами Апостола-Ейлера i q-дзета-функцією Хурвіца-Лерча

Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas for the convolutions of Bernoulli and Euler polynomials, expressed via Apostol-Bernoulli polynomials of higher order.Comment: 8 pages, submitte

Some New Symmetric Identities for the q-Zeta Type Functions

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 applications are shown to lead to a number of interesting results which we state in the present paper.Comment: 8 pages; submitte

Special Functions Related to Dedekind Type DC-Sums and their Applications

In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions