Şimşek, YılmazKurt, VeliKim, Daeyeoul2022-03-312022-03-312008Şimşek, Y. vd. (2008). "q-Genocchi numbers and polynomials associated with q-Genocchi-type l-functions". Advances in Difference Equations.N1687-1839https://doi.org/10.1155/2008/815750https://advancesindifferenceequations.springeropen.com/articles/10.1155/2008/815750http://hdl.handle.net/11452/25478The main purpose of this paper is to study on generating functions of the q-Genocchi numbers and polynomials. We prove new relation for the generalized q-Genocchi numbers which is related to the q-Genocchi numbers and q-Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define q-Genocchi zeta and l-functions, which are interpolated q-Genocchi numbers and polynomials at negative integers. We also give some applications of generalized q-Genocchi numbers.eninfo:eu-repo/semantics/openAccessQ-bernoulli numbersQ-euler numbersBasic l-seriesQ-analogMathematicsArticle0002566706000012-s2.0-46649120845Mathematics, appliedMathematicsEuler Polynomials; Bernoulli Numbers; P-Adic Q-Integral