The sign regularity of the auxiliary family gi(x) = xαi(−ln x)βi in convergence acceleration processes using the E-algorithm

The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition. In this work it is proved that such condition is fulfilled for any error expansion in which formation enter the auxiliary family hnαi(−lnhn)βi (where hn designates the stepsize of the discretization method).