We present a method of estimating perturbative coefficients in Quantum Field Theory using Padé Approximants. We test this method on various known QCD results, and find that the method works very well. ? Work supported by the Department of Energy, contract DE–AC03–76SF00515. † To appear in Phys. Rev. Lett. By using the first n coefficients in a series expansion, we have estimated the (n+ 1)-st p...

The power series in the coupling constant g or in ε derived so far are unsuitable for numeric calculations since they are divergent for any coupling strength. They are called asymptotic series. Resummation procedures are necessary to extract physical results. The crudest method to approximate a divergent function f (g) whose first L expansion coefficients are known employs Padé approximants [1]...

We consider the model problem of mixing passive tracers by an incompressible viscous fluid. Addressing questions optimal control in realistic geometric settings or alternatively design fluid-confining geometries that successfully effect requires a meaningful norm which to quantify is also suitable for easy and efficient computation (as needed, e.g., use gradient-based optimization methods). phy...

Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish a more accurate formula for approximating π, which refines some known results.

A reduced order multiport modeling algorithm based on the decomposition of the system transfer matrix into orthogonal scaled Laguerre functions is proposed. The link with Padé approximation, the block Arnoldi method and singular value decomposition leads to a simple and stable implementation of the algorithm.

An algorithm for a Pick-Nevanlinna problem where the interpolation points coalesce into a finite set of points on the real line is introduced, its connection with certain multipoint Padé approximation problems is discussed, and the results are used to obtain the solutions of an extended Hamburger moment problem.

We solve the equation of the title for q = 3 and, partially, for q = 2. These are the only prime values of q for which there exist integer solutions. Our arguments are based upon off-diagonal Padé approximation to the binomial function.