A note on the generalized q-Genocchi measures with weight

Hassan Jolany; Serkan Araci; Mehmet Acikgoz; Jong-Jin Seo

doi:10.5269/bspm.v31i1.14184

Hassan Jolany University of Tehran School of Mathematics, Statistics and Computer Science
Serkan Araci University of Gaziantep Faculty of Science and Arts Department of Mathematics
Mehmet Acikgoz University of Gaziantep Faculty of Science and Arts Department of Mathematics
Jong-Jin Seo Pukyong National University Department of Applied Mathematics

DOI: https://doi.org/10.5269/bspm.v31i1.14184

Keywords: Genocchi numbers and polynomals, q-Genocchi numbers and polynomials, q-Genocchi numbers and polynomials with weight alpha

Abstract

In this paper we investigate special generalized q-Genocchi measures. We introduce q-Genocchi measures with weight alpha. 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 alpha which yields a deeper insight into the effectiveness of this type of generalizations. Generalized q-Genocchi numbers with weight alpha possess a number of interesting properties which we state in this paper.

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