Increasing the convergence rate of series
A method of accelerating the speed of convergence of a given series is presented and demonstrated by several examples. The main assumption is the existence of a specific asymptotic expansion of the terms in the series. In the examples the method works quite well. The paper does not contain proofs or theoretical backgrounds. The list of references only consists of papers of the author, except for the Handbook of mathematical functions (1967; Zbl 0171.385) by \textit{M. Abramowitz} and \textit{I. A. Stegun}. Other publications of similar content and close connection to the topic of the paper are not found under the references, and are not referred to in the text, e.g. \textit{J. Wimp} [SIAM J. Numer. Anal. 14, 194-204 (1977; Zbl 0355.65003)], \textit{A. H. Stroud} [Numerical quadrature and solution of ordinary differential equations (1974; Zbl 0298.65018), in particular p. 145-162], \textit{C. Brezinski} [Numer. Math. 35, 175-187 (1980; Zbl 0444.65001)], the reviewer [Proc. 5th South Afr. Symp. Numerical mathematics, Durban 1979, 1-20 (1979; Zbl 0435.65100)], the reviewer and \textit{G. Merz} [Praktische Mathematik. II. (1982; Zbl 0476.65001), in particular chapter 12].
scientific article; zbMATH DE number 4030799