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arXiv · 1312.0255

Identities involving the $\left(h,q\right)$-Genocchi polynomials and $\left(h,q\right)$-Zeta-type function

Armen Bagdasaryan·Erdogan Sen·Yuan He·Serkan Araci·Mehmet Acikgoz
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Abstract

The fundamental objective of this paper is to obtain some interesting properties for $\left(h,q\right)$-Genocchi numbers and polynomials by using the fermionic $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and mentioned in the paper $q$-Bernstein polynomials. By considering the $q$-Euler zeta function defined by T. Kim, which can also be obtained by applying the Mellin transformation to the generating function of $\left(h,q\right)$-Genocchi polynomials, we study $\left(h,q\right)$-Zeta-type function. We derive symmetric properties of $\left(h,q\right)$-Zeta function and from these properties we give symmetric property of $\left(h,q\right)$-Genocchi polynomials.

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Armen Bagdasaryan, Erdogan Sen, Yuan He, Serkan Araci, Mehmet Acikgoz. 2013-12-01. Identities involving the $\left(h,q\right)$-Genocchi polynomials and $\left(h,q\right)$-Zeta-type function. https://arxiv.org/abs/1312.0255

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