On continued fractions corresponding to asymptotic series
Simple conditions on a sequence of functions \(f_ n\) with contact of order \(k_ n\to \infty\) with a formal power series for the power series to be asymptotic to a function f are established. The conditions are in terms of estimates on the differences of f and \(f_ n\) and \(f_ m\) and \(f_ n\) in terms of each other. These conditions are used to give a unification of some results for continued fractions and asymptotic expansions for their limit.
scientific article; zbMATH DE number 3912691