Inequalities for Residuals of Power Expansions for the Exponential Function and Completely Monotone Functions*

Let In x. be the residual after the nth term of power series for a function f. In the case f x.se x, x)0, inequalities for In have been studied by many authors, but there are almost no results for x-0. In this paper we present some bounds for In with f x.seyx and we give some results for completely monotone functions