In this paper, the Fourier series expansion of Tangent polynomials higher order is derived using Cauchy residue theorem. Moreover, some variations higher-order are defined by mixing concept with that Bernoulli and Genocchi polynomials, Tangent–Bernoulli Tangent–Genocchi polynomials. Furthermore, expansions these also

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In [2], we introduced the q-Genocchi numbers and polynomials with weak weight α. In this paper, we investigate some properties which are related to q-Genocchi numbers G (α) n,q and polynomials G (α) n,q (x) with weak weight α.

In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite-Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained ...

where we use the technical method’s notation by replacing G x by Gn x , symbolically, see 1, 2 . In the special case x 0, Gn Gn 0 are called the nth Genocchi numbers. From the definition of Genocchi numbers, we note that G1 1, G3 G5 G7 · · · 0, and even coefficients are given by G2n 2 1 − 22n B2n 2nE2n−1 0 see 3 , where Bn is a Bernoulli number and En x is an Euler polynomial. The first few Gen...

In this work, we consider variable order difusion and wave equations. The derivative is describedin the Caputo sence of variable order. We use the Genocchi polynomials as basic functions andobtain operational matrices via these polynomials. These matrices and collocation method help usto convert variable order diusion and wave equations to an algebraic system. Some examples aregiven to show the...

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.

Inspired by a number of recent investigations, we introduce the new analogues of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, the Apostol-Genocchi polynomials based on Mittag-Leffler function. Making use of the Caputo-fractional derivative, we derive some new interesting identities of these polynomials. It turns out that some known results are derived as special cases.

In this paper we construct q-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the q-analogue of alternating sums of powers of consecutive integers due to Euler. 2000 Mathematics Subject Classification : 11S80, 11B68

We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.

In the paper, we derive some new symmetric identities of q-Genocchi polynomials arising from the fermionic p-adic q-integral on Zp.