New Symmetric Identities Involving q-Zeta Type Functions

Abstract

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. RésuméL'objet principal de cet article est d'obtenir plusieurs propriétés symétriques des fonctions de type q-Zeta. Comme les applications de ces propriétés, nous donnons quelques nouvelles identités intéressantes pour les polynômes q-Genocchi modifiés. Enfin, nos applications sont présentésà conduireà un certain nombre de résultats intéressants que nous disons dans le présent document.

On the Properties of q-Bernstein-type Polynomials

“…The Euler numbers are defined by E n (1/2) = 2 n E n . The Euler polynomials can be generated through Equation (for details, see [6], [8], [9], [13], [15], [22], [28], [29], [30]). In [22], Kim defined the following q-Euler numbers…”

“…, (see [4], [5], [6], [19], [20], [17], [21], [31], [38], [39], [40] for details and related facts). Note that lim [19] is actually motivated the authors to write this paper and they have extended all results given in [19] to modified q-Bernstein polynomials of several variables.…”

A new generalization of Apostol type Hermite–Genocchi polynomials and its applications

“… 2014 ; Agarwal and Koul 2003 ; Apostol 1951 ; Araci 2014 ; Araci et al. 2014a , b ; Bell 1934 ; Dattoli et al. 1999 ; Dere and Simsek 2015 ; Dere et al.…”

“… By using the modified Milne-Thomson’s polynomial given in Araci et al (Appl Math Inf Sci 8(6):2803–2808, 2014 ), we introduce a new concept of the Apostol Hermite–Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method.…”

Identities of Symmetry for the Generalized Degenerate Euler Polynomials

“…When x = 0, E n = E n (0) are called the Euler numbers (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). For a fixed odd integer d with (p, d) = 1, we set…”