Full asymptotic expansions of the Landau constants via a difference equation approach

摘要

We derive full asymptotic expansions for the Landau constants Gn as n→∞. Some of the expansions are not new, yet all the coefficients of the expansions are given iteratively in an explicit manner, and are more efficiently evaluated as compared with the known results. We obtain the asymptotic formulas, old and new, by applying the theory of Wong and Li for second-order linear difference equations. In deriving the expansions, we have also confirmed a conjecture made by Nemes and Nemes.