Elementary remarks on multiply monotonic functions and sequences

1. Introduction and statement of results. A function f(x) is said to be completely monotonie on (0, oo) if (1) (-l)n / ( n)(*)> 0 (0 < x < oo; n = 0, 1, 2,...). Familiar examples of such functions are given by /(x) = exp(—ax) and f(x) = (x+f$)~a, where a>0, £>0. A discussion of completely monotonie functions i