In this study, differential transform method (DTM) is applied to fuzzy integro-differential equation. The concept of generalized Hdifferentiability is used. If the equation has a solution in terms of the series expansion of known functions; this powerful method catches the exact solution. Some numerical examples are also given to illustrate the superiority of the method. All rights reserved.

The univariate theorem deals with the case of simple poles as well as with the case t multiple poles. The former means that we have information on the denominator of th meromorphic function while the latter means that we also have information on the derivative ef that denominator. Up to now w-e o+ ,...; prtivcd a multivariate analogon of the univariate d Montessus dc Baiiore theorem for the cas...

The validity of a series expansion proposed previously @T. H. Jensen and M. S. Chu, Phys. Fluids 27, 2881 ~1984!# for describing general Taylor configurations of magnetized plasmas has been reexamined because an apparent paradox was realized. From analyses of simple cases which can be dealt with mostly analytically, it is concluded that the paradox is a Gibbs phenomenon, and that the series exp...

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal .

The problem to decide whether a given multivariate (quasi-)rational function has only positive coefficients in its power series expansion has a long history. It dates back to Szegö [10], who showed that ((1−Z1)(1−Z2) + (1−Z1)(1−Z3) + (1−Z2)(1−Z3)) for β ≥ 1/2 is positive, in the sense that all its series coefficients are positive, using an involved theory of special functions. In contrast to th...

We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a nonmean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occurring in the usual m...

Selection of some of the numerous series expansion involving the famous constant π.

In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the dimension is infinite. We develop the perturbation theory systematically for calculating von Neumann entropy of non-degenerate systems as well as degenerate s...

We show how to find series expansions for π of the form π = ∞ n=0 S(n) mn pn a n , where S(n) is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for m = 8k, p = 4k, a = (−4) k , for any k, and give explicit examples for such expansions for small values of m, p and a.

The purpose of this paper is to initiate the study of a new kind of asymptotic series expansion for solutions of differential equations containing a parameter. We obtain uniform asymptotic solutions for certain equations of the form ê»y" = ait, e)y , ( )' = d/dt, where n is a positive integer, t and e are real variables ranging over \t\ S U, 0 < e ^ €o, and a is a function infinitely differenti...