Based on the blossoming theory, in this work we develop a new method for deriving Hermite-Padé approximants of certain hypergeometric series. Its general principle consists building identities generalising Hermite identity exponentials, and then applying their blossomed versions to appropriate tuples simultaneously produce explicit expressions integral representations corresponding remainders. ...

The extended quasiparticle picture is adapted to non-Fermi systems by suggesting a Pad\'e approximation which interpolates between the known small scattering-rate expansion and deviation from Fermi energy. first two energy-weighted sum rules are shown be fulfilled independent of interpolating function for any selfenergy. For various models one-dimensional Fermions scattering with impurities qua...

Padé 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 general method, we will review a number of recent applications and describe the modifications that have to be applied in each case. Among these applications are...