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

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.

14 pages; submitted

References in corpus (4)

• A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
• Identities involving values of Bernstein, q-Bernoulli and q-Euler polynomials
• Elementary Evaluation of the Zeta and Related Functions
• On p-adic analogue of q-Bernstein polynomials and related integrals