A one-parameter method for accelerating the convergence of sequences and series

AbstractAn iterative non-stationary method, depending on a parameter, has been obtained for accelerating the convergence of power series. When the parameter is equal to + 1, the method of Salzer and Szász[4, 6] is recovered (called Method A), and when the parameter is equal to the argument of the power series, rational approximations are obtained, although not as good as Padé approximants. When the parameter is equal to − 1, the method (called Method B) effects more rapid convergence on well-known alternating series than any of the methods commonly used hitherto