On the modified q-Genocchi numbers and polynomials and their applications

Aracı, Serkan; Bagdasaryan, Armen; Agyuz, Erkan; Açıkgöz, Mehmet

doi:10.48550/arxiv.1311.5992

Cited by 1 publication

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“…From Genocchi to the present time, the Genocchi polynomials and the Genocchi numbers have been extensively studied in many different contexts in such branches of Mathematics as, for instance, Elementary Number Theory, Complex Analytic Number Theory, Homotopy Theory (especially stable Homotopy groups of spheres), Differential Topology (especially differential structures on spheres), Theory of Modular Forms (especially Eisenstein series), p-Adic Analytic Number Theory (especially p-adic L-functions) and Quantum Physics (especially quantum groups). Investigations involving the Genocchi polynomials and their associated combinatorial relations have received considerable attention in recent years (see, for details, [1], [4], [5], [6], [14], [22], [28] and [24]).…”

Section: Introductionmentioning

confidence: 99%

“…Araci et al [4] studied the modified q-Genocchi polynomials which are given by the following generating function:…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, Araci et al [4], Araci introduced the q-Zeta type function ζ q (s, x) which is slightly different from Kim's q-Zeta function ζ q (s, x) defined by (1.7):…”

Section: Introductionmentioning

confidence: 99%

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Appl. Math. Inf. Sci.

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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.

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