Two Applications of Approximate Differentiation Formulae: An Extremum Problem for Multiply Monotone Functions and the Differentiation of Asymptotic Expansions

摘要

This report presents two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of a theorem of V. M. Olovyanisnikov on multiply monotone functions. The second applications gives sufficient conditions for the differentiability of asymptotic expansions.