A note on the generalized q-Genocchi measures with weight α

Abstract

In this paper we investigate special generalized q-Genocchi measures. We introduce q-Genocchi measures with weight α. The present paper deals with q-extension of Genocchi measure. Some earlier results of T. Kim in terms of q-Genocchi polynomials can be deduced. We apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi measures. To be more precise, we present the integral representation of p-adic q-Genocchi measure with weight α which yields a deeper insight into the effectiveness of this type of generalizations. Generalized q-Genocchi numbers with weight α possess a number of interesting properties which we state in this paper. © Soc. Paran. de Mat.