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Many kinds of generalizations of these polynomials and numbers have been presented in the literature (see [1,2]). Bayad and Hamahata in [1] introduced and investigated the poly-Bernoulli polynomials and proved some relations for these polynomials. Cenkci and Kamatsu in [3] are defined q-parameter poly-Bernoulli numbers. They proved some relations between these polynomials. Kim et al. in ([4,5]) defined poly-Genocchi polynomials and gave the some properties for the multiple-poly-Bernoulli numbers and multiple-zeta values. We introduce the Hermite-based poly-Genocchi polynomials with a q-parameter. After, we give and investigate some properties and identities for these polynomials. Furthermore, we prove closed formula and two explicit relations.

On the Hermite-Based Poly-Genocchi Polynomials with a q-Parameter