Let [Sn] n=0 be such that Sn tS+ j=1 aj* n j as n , with 1>|*1 |> |*2 |> } } } , such that limj *j=0. A well-known result by Wynn states that when the Shanks transformation or its equivalent =-algorithm is applied to [Sn] n=0 , then = (n) 2k &Stak+1[> k i=1 (*k+1&*i) (1&*i)] 2 *k+1 as n . In the present work we extend this result (i) by allowing some of the *j to have the same modulus and (ii) ...

We present a critical analysis of Padé-based methods for the unitarization of low energy amplitudes. We show that the use of certain Padé Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method produces essentially incorrect result...

In order to calculate the energy when 0127 is small, we expand the right-hand side of the BrillouinWigner equation in terms of a coupling constant 03BB. Both hierarchies in 0127 and 03BB are connected. The Padé approximants of the right-hand side converge. Tome 40 N° 2 15 JANVIER 1979 LE JOURNAL DE PHYSIQUE LETTRES

The relation between the on-shell and MS mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at three-loop order. Instead, we evaluate the quark self energy in the limit of large and small external momentum and use conformal mapping in combination with Padé improvement in o...

In a previous paper, the author introduced a class of multivariate rational interpolants, which are called optimal Padé-type approximants (OPTA). The main goal of this paper is to extend classical results on convergence both in measure and in capacity of sequences of Padé approximants to the multivariate case using OPTA. To this end, we obtain some estimations of the size of multivariate polyno...