For a large class of two-loop selfenergyand vertex-type diagrams with only one nonzero mass (M) and the vertices also with only one non-zero external momentum squared (q2) the first few expansion coefficients are calculated by the large mass expansion. This allows to ‘guess’ the general structure of these coefficients and to verify them in terms of certain classes of ‘basis elements’, which are...

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

Conditions are determined under which 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) is a monotone function of n satisfying ab· 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) ≥ ab· 2F1 (a, b; a + b + 2; 1) . Motivated by a conjecture of Vuorinen [Proceedings of Special Functions and Differential Equations, K. S. Rao, R. Jagannathan, G. Vanden Berghe, J. Van der Jeugt, eds., Allied Publishers, New Delhi, 1998...

There are many studies to approximate sine curve or wave. In this study, it has been examined the way how wave can be written as any order Bezier curve. First, 5th and 7th degree Maclaurin series expansion of parametric form Also, they paths, based on control points with matrix in E2. Hence given coefficients curves three steps. Further too.

In the real world, there are many applications that find Pascal distribution to be a useful and relevant model. One of these is normal distribution. this work, we develop new subclass analytic bi-univalent functions by making use q-Pascal series as construction. These involve q-Gegenbauer polynomials, them establish our subclass. Moreover, solve Fekete–Szegö functional problem analyze various d...

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, ...

With the Fast Fourier Transform (FFT), a mathematical model for accurately computing distribution of a lightning currents flowing along a high voltage a.c. substation’s grounding system buried in half infinite homogenous earth has been developed in this paper. It is a hybrid of Galerkin’s method of moment (MoM) and a conventional nodal analysis method. The model can directly calculate the distr...

The central bank’s monetary policy targets are usually assumed to be constant overtime for simplicity when estimating a Taylor rule, but recent studies have shed some light on the time variation in policy targets, especially in the inflation target. The potential bias due to misspecification of the time variation can be quite considerable, especially in regime-swtiching models. In this paper, w...

One of the most common and practical ways of representing a real function on machines is by using a polynomial approximation. It is then important to properly handle the error introduced by such an approximation. The purpose of this work is to offer guaranteed error bounds for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq proof assis...