Effiziente Berechnung spezieller Funktionen mittels asymptotischer Entwicklungen und Eliminationsprozeduren

Abstract

In this paper we suggest a method for the approximation of functions, which differs on principle from the usual approximation methods (polynomial and rational approximations, splines); it can be applied to a great variety of functions, e.g., the natural logarithm, inverse circular, and hyperbolic functions and elliptic integrals of the first kind. Many numerical examples and comparisons, e.g., with the method of arithmetic-geometric mean, illustrate the efficiency of our method.