Şimşek, YılmazSrivastava, Hari M.2021-10-252021-10-252010-11Özden, H. vd. (2010). "A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials". Computers & Mathematics with Applications, 60(10), 2779-2787.0898-12211873-7668https://doi.org/10.1016/j.camwa.2010.09.031https://www.sciencedirect.com/science/article/pii/S0898122110007170http://hdl.handle.net/11452/22461The goal of this paper is to unify and extend the generating functions of the generalized Bernoulli polynomials, the generalized Euler polynomials and the generalized Genocchi polynomials associated with the positive real parameters a and b and the complex parameter beta. By using this generating function, we derive recurrence relations and other properties for these polynomials. By applying the Mellin transformation to the generating function of the unification of Bernoulli, Euler and Genocchi polynomials, we construct a unification of the zeta functions. Furthermore, we give many properties and applications involving the functions and polynomials investigated in this paper.eninfo:eu-repo/semantics/closedAccessBernoulli numbers and Bernoulli polynomialsEuler numbers and Euler polynomialsGenocchi numbers and Genocch polynomialsRiemann and Hurwitz (or generalized) zeta functionsHurwitz-Lerch zeta functionLerch zeta functionPolylogarithm functionLipschitz-Lerch zeta functionRecurrence relationsMellin transformationDirichlet characterApostol-bernoulliZetaNumbersExtensionFormulasMathematicsFunction evaluationFunctionsPolynomialsBernoulli polynomialsDirichlet charactersEuler numbersLerch zeta functionMellin transformationPolylogarithm functionsRecurrence relationsZeta functionNumber theoryArticle0002846561000062-s2.0-78049294653277927876010Mathematics, appliedEuler Polynomials; Bernoulli Numbers; P-Adic Q-Integral