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arxiv: 1312.0255 · v1 · pith:HDOPLFVPnew · submitted 2013-12-01 · 🧮 math.NT

Identities involving the left(h,qright)-Genocchi polynomials and left(h,qright)-Zeta-type function

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keywords leftrightfunctionpolynomialsgenocchipropertiessymmetriczeta
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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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