We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the q-case have previously been obtained by Cooper and by Ismail and Stanton. We also provide identities involving S. Bhargava’s cubic theta functions.

The paper presents the design of nonlinear state feedback controller for a rigid manipulator. In order to obtain such controllers, a partial differential equation, HJB equation, should be solved, which is difficult to find a closed solution of that. In this paper, an efficient method using Taylor series expansion of nonlinear terms is used to tackle this problem. The tracking performance of the...

An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several coefficients of the Taylor series expansion for the two-loop non-planar vertex and two-loop propagator diagrams are calculated. The results of the numerical eva...

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...

In a recent paper [1] a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero. It was demonstrated that by a certain conformal mapping and subsequent resummation by means of...

The Taylor expansion of λ-terms, as introduced by Ehrhard and Regnier, expresses a λ-term as a series of multi-linear terms, called simple terms, which capture bounded computations. Normal forms of Taylor expansions give a notion of infinitary normal forms, refining the notion of Böhm trees in a quantitative setting. We give the algebraic conditions over a set of normal simple terms which chara...

The Taylor expansion has shown in many fields to be an extremely powerful tool. In this paper, the authors investigated image features and their relationships by analogy with Taylor expansion. The kind of expansion could be helpful for analyzing image feature and engraftment, such as transferring color between images. By analogy with Taylor expansion, the image color transfer algorithm is desig...

a simple mathematical model of steady state  oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. the approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. the computational results for the scaled variables are presented through graphs. the effect of the important parameters (1) d...

In this paper a computational algorithm for nonlinear balanced realization and model reduction based on Taylor series expansion is proposed. This algorithm requires recursive computations with respect to the order of the Taylor series in which we need to solve linear equations with unknown parameters in each step. Furthermore, the proposed method is applied to a double pendulum system. Some num...