The known proofs for universal Taylor series do not determine a specific universal Taylor series. In the present paper, we isolate a specific universal Taylor series by modifying the proof in [30]. Thus we determine all Taylor coefficients of a specific universal Taylor series on the disc or on a polygonal domain. Furthermore in non simply connected domains, when universal Taylor series exist, ...

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

We derive the MacLaurin series for the moments of the system time and the delay with respect to the parameters in the service time or interarrival time distributions in the GI/G/1 queue. The coe cients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calcula...

In this article we introduce three new subclasses of the class bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using subordinations with whose coefficients are Gregory numbers. First, evidence that these classes not empty, i.e., they contain other besides identity one. For in each function classes, investigate estimates a2 a3 Taylor–Maclaurin Fekete–Szegő functional problems. The mai...