We obtain results on the convergence of Padé approximants of Stieltjes-type meromorphic functions and the relative asymptotics of orthogonal polynomials on unbounded intervals. These theorems extend some results given by Guillermo López in this direction substituting the Carleman condition in his theorems by the determination of the corresponding moment problem. c © 2009 Elsevier Inc. All right...

Part I of this paper embeds the AC power flow problem with voltage control and exponential load model in the complex plane. Modeling the action of network controllers that regulate the magnitude of voltage phasors is a challenging task in the complex plane as it has to preserve the framework of holomorphicity for obtention of these complex variables with fixed magnitude. The paper presents two ...

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series expansions of rational functions exhibit almost cancelling polezero combinations that are unwanted. The location of these pole-zero pairs is given by the socalled Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in...

In this paper, we present rational approximations based on Fourier series representation. For periodic piecewise analytic functions, the well-known Gibbs phenomenon hampers the convergence of the standard Fourier method. Here, for a given set of the Fourier coefficients from a periodic piecewise analytic function, we define Fourier–Padé–Galerkin and Fourier–Padé collocation methods by expressin...

Boyd shows in [3] that for a function with singularities in the imaginary plane, the Gegenbauer expansion of the function may have Runge-type oscillations so large that all hope of convergence for the method is lost. We consider the use of Padé-Gegenbauer interpolants to resolve these oscillations. We describe a fast interpolation-based reconstruction for computing the Padé-Gegenbauer approxima...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive upper bounds for the irrationality exponent of famous automatic real numbers associated with the Thue–Morse, Rudin–Shapiro, paperfolding and Baum–Sweet sequences. These upper bounds arise from the construction o...

In 1961, Baker, Gammel and Wills conjectured that for functions f meromorphic in the unit ball, a subsequence of its diagonal Padé approximants converges uniformly in compact subsets of the ball omitting poles of f . There is also apparently a cruder version of the conjecture due to Padé himself, going back to the early twentieth century. We show here that for carefully chosen q on the unit cir...

An approximation algorithm is proposed to transform truncated QCD (or QED) series for observables. The approximation is a modification of the Baker–Gammel approximants, and is independent of the renormalization scale (RScl) µ – the coupling parameter α(µ) in the series and in the resulting approximants can evolve according to the perturbative renormalization group equation (RGE) to any chosen l...

Padé approximants are used to improve the convergence behavior of perturbative results in massless scalar and gauge field theories at finite temperature. In recent years, computational methods have been developed to analytically tackle three-loop vacuum diagrams and higher-order contributions of diagrams with less loops in massless field theories at finite temperature [1]-[5]. Consequently, the...