Şimşek, Yılmaz2024-02-152024-02-152014-04-22Özden, H. ve Şimşek, Y. (2014). "Unified presentation of p-adic L-functions associated with unification of the special numbers". Acta Mathematica Hungarica, 144(2), 515-529.0236-5294https://link.springer.com/article/10.1007/s10474-014-0446-9https://hdl.handle.net/11452/39734By using partial differential equations (PDEs) of the generating functions for the unification of the Bernoulli, Euler and Genocchi polynomials and numbers, we derive many new identities and recurrence relations for these polynomials and numbers. In [33], Srivastava et al. defined a unified presentation of certain meromorphic functions related to the families of the partial zeta type functions. By using these functions, we construct p-adic functions which are related to the partial zeta type functions. By applying these p-adic function, we construct unified presentation of p-adic L-functions. These functions give us generalization of the Kubota-Leopoldt p-adic L-functions, which are related to the Bernoulli numbers and the other p-adic L-functions, which are related to the Euler numbers and polynomials. We also give some remarks and comments on these functions.eninfo:eu-repo/semantics/closedAccessBernoulli number and polynomialEuler number and polynomialGenerating functionGenocchi number and polynomialP-adic functionPartial differential equation (pde)P-adic l-functionPartial zeta type functionRiemann and hurwitz (or generalized) zeta functionGenerating-functionsQ-analogFamiliesEuler(h)BernoulliSeriesPolynomialsExtensionBehaviorMathematicsArticle0003445781000122-s2.0-850281115765155291442https://doi.org/10.1007/s10474-014-0446-9MathematicsEuler Polynomials; Bernoulli Numbers; Degenerate1588-2632