Related papers: Asymptotic Pad\'e Approximants and the SQCD $\beta…
We obtain the strong asymptotics of multiple orthogonal polynomials which arise in a mixed type Hermite-Pad\'e approximation problem defined on a Nikishin system of functions. The results obtained allow to give exact estimates of the rate…
The effective charges motivated method is applied to the relation between pole and $\rm{\overline{MS}}$-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running…
Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…
Three-loop quantum corrections to the effective action are calculated for N=1 supersymmetric electrodynamics, regularized by higher derivatives. Using the obtained results we investigate the anomaly puzzle in the considered model.
We have obtained the exact asymptotics of the determinant $\det_{1\leq r,s\leq L}[\binom{r+s-2}{r-1}+\exp(i\theta)\delta_{r,s}]$. Inverse symbolic computing methods were used to obtain exact analytical expressions for all terms up to…
The perturbation series for the renormalization group functions of the $O(N)-$symmetric $\phi^4$ field theory are divergent but asymptotic. They are usually followed by Resummation calculations to extract reliable results. Although the same…
We investigate the asymptotic behavior of the polynomials p, q, r of degrees n in type I Hermite-Pade approximation to the exponential function, defined by p(z)e^{-z}+q(z)+r(z)e^{z} = O(z^{3n+2}) as z -> 0. These polynomials are…
We verify a recently proposed method for obtaining a $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a $\beta$-function can be found by…
Pade approximations appear to be a powerful tool to extend the validity range of expansions around certain kinematical limits and to combine expansions of different limits to a single interpolating function. After a brief outline of the…
Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a…
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve…
In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop $\beta$-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part,…
Based on the compilation of the available e^+e^- data, we present a non-perturbative estimation of the Adler function derived from the electromagnetic current correlator, and compare it with theoretical predictions from perturbative QCD…
The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, {\it the so-called uniform asymptotic…
In this paper a recursive algorithm is presented for evaluating multivariate Pad\'e approximants (of the rectangular type described in the work of Lutterodt) which is analogous to the Jacobi formula for univariate Pad\'e approximants. This…
Technical aspects of the Shirkov-Solovtsov's analytic perturbation theory (APT) are considered. We construct explicitly two sets of specific functions, ${\mathfrak{A}_n(s)}$ and ${{\cal A}_n(Q^2)}$ that determine the nonpower as ymptotic…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
New asymptotic relations between the $L_p$-errors of best approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for $p\in (0,\iy]$. General asymptotic relations are applied to…
We compute the four-loop corrections to the Higgs-bottom vertex within massless QCD and present analytic results for all color structures. The infrared poles of the renormalized form factor agree with the predicted four-loop pattern.…
By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in…