For , the generalized Mittag-Leffler function is defined as
It was proved by H. Pollard [Bull. Am. Math. Soc. 54, 1115-1116 (1948; Zbl 0033.35902)] that for the function is completely monotonic for ; W. R. Schneider [Expo. Math. 14, No. 1, 3-16 (1996; Zbl 0843.60024)] improved this by showing that is completely monotone on if and . In the present note the author shows that the latter result is in fact a simple consequence of the former.