We use Asymptotic Padé Approximants (APAP’s) to predict the fourand five-loop β functions in QCD and N = 1 supersymmetric QCD (SQCD), as well as the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories. We show how the accuracy of our previous β-function predictions at the four-loop level may be further improved by using estimators weighted over negative numbers of flavours...

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so-called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the ...

We will consider variational iteration method VIM and Padé approximant, for finding analytical solutions of the Glauert-jet self-similar wall jet over an impermeable, resting plane surface problem. The solutions are compared with the exact solution. The results illustrate that VIM is an attractive method in solving the systems of nonlinear equations. It is predicted that VIM can have a found wi...

Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing A e and for computing At e with many 0 t  re...

The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the MS series for the QCD static potential are calculated and compared to values obtained via asymptotic Padé-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Padé-predictions. The predicted value for the thi...

The Padé table of 2F1(a, 1; c; z) is normal for c > a > 0 (cf. [4]). For m ≥ n−1 and c / ∈ Z − , the denominator polynomial Qmn(z) in the [m/n] Padé approximant Pmn(z)/Qmn(z) for 2F1(a, 1; c; z) and the remainder term Qmn(z)2F1(a, 1; c; z)−Pmn(z) were explicitly evaluated by Padé (cf. [2], [6] or [9]). We show that for c > a > 0 and m ≥ n−1, the poles of Pmn(z)/Qmn(z) lie on the cut (1,∞). We d...

Based on the Padé approximation method, we determine the coefficients [Formula: see text] and [Formula: see text] ([Formula: see text]) such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish new bounds for the gamma function.