A detailed analysis to the [1,2] Padé approximation to the ππ scattering 2–loop amplitudes in chiral perturbation theory is made.

The learning capability of a network-based computation model named “Algorithmically Transitive Network (ATN)” is extensively studied using symbolic regression problems. To represent a variety of functions uniformly, the ATN’s topological structure is designed in the form of a truncated power series or a Padé approximant. Since the Padé approximation has better convergence properties than the Ta...

In this paper, we investigate the quality of the moments based Padé approximation of ultimate ruin probabilities by exponential mixtures. We present several numerical examples illustrating the quick convergence of themethod in the case of Gammaprocesses. While this is not surprising in the completely monotone case (which holds when the shape parameter is less than 1), it is more so in the oppos...