Asymptotic Padé-approximant methods are utilized to estimate the O(α5s) contribution to the H → gg rate and the O(α4s) contribution to the H → bb̄ rate. The former process is of particular interest because of the slow convergence evident from the three known terms of its QCD series, which begins with an O(α2s) leading-order term. The O(α5s) contribution to the H → gg rate is expressed as a degre...

Article history: Received 9 July 2010 Received in revised form 1 October 2010 Accepted 4 October 2010 Available online 12 October 2010

The response function for a general class of elastic molecular based materials characterized by their limiting molecular chain extensibility and depending on only the first principal invariant of the Cauchy–Green deformation tensor together with a certain molecular based limiting extensibility parameter is introduced. The constitutive response function for the Gent material is then derived inve...

Within the context of massive N -component φ scalar field theory, we use asymptotic Padéapproximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant β-function βg, the anomalous mass dimension γm, the vacuum-energy βfunction βv, and the anomalous dimension γ2 of the scalar field propagator. These estimates are then compared with e...

Abstract. The convergence of a Fourier series on an interval can be interpreted naturally as the convergence of a Laurent series on the unit circle in the complex plane. In turn this Laurent series can be interpreted as the sum of an analytic and a co-analytic Taylor series.The Gibbs phenomenon in this context can be seen as an attempt to approximate a logarithmic branch cut with such series. C...

Given a function f holomorphic at infinity, the n-th diagonal Padé approximant to f, denoted by [n/n]f, is a rational function of type (n,n) that has the highest order of contact with f at infinity. Nuttall’s theorem provides an asymptotic formula for the error of approximation f− [n/n]f in the case where f is the Cauchy integral of a smooth density with respect to the arcsine distribution on [...