CERTAIN RESULTS ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS

Abstract

Abstract. In this work, we deal with q-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the q-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the q-Genocchi polynomials and derive distribution formula for the q-Genocchi polynomials. In the final part, we introduce a definition of q-Zeta-type function which is interpolation function of the q-Genocchi polynomials at negative integers which we express in the present paper.

Existence and Uniqueness of Positive Solutions of Boundary-Value Problems for Fractional Differential Equations withp-Laplacian Operator and Identities on the Some Special Polynomials

“…(see [35]). Obviously, we have that In the region = { ∈ C | | | < }, Genocchi polynomials, ( ), and Genocchi polynomials of higher order, ( ) ( ), are defined as an extension of Genocchi numbers defined in [33,37,38], respectively,…”