Study of a generalized Levin–Weniger convergence accelerator of numerical series: Particular cases and applications to multi-electron integrals in atomic physics

In this work the general Levin transformation for a new remainder estimate is studied and compared to the u-transformation for some particular test cases. Also, the Weniger transformation and a generalization of both are studied specifically for the three-electron problem in atomic physics. In addition, we study the problem of the instability of these convergence accelerators and discuss attempts to reduce them.